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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2, Problem 28RE

Textbook Problem

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**Determining Differentiability** In Exercises 25–28, describe the *x*-values at which the function is differentiable. Explain your reasoning.

Expert Solution

To determine

The value of

**Given Information:**

The provided function is

Consider the provided function is

The provided graph is shown below:

A function is not differentiable at the point on its graph (which must be continuous for all the values of *x* in in the function’s domain) at which a cusp is formed

Calculus: An Applied Approach (MindTap Course List)

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In Exercises 69-72, determine...Ch. 2.1 - True or False? In Exercises 69-72, determine...Ch. 2.1 - True or False? In Exercises 69-72, determine...Ch. 2.1 - True or False? In Exercises 69-72, determine...Ch. 2.1 - Writing Use a graphing utility to graph the two...Ch. 2.2 - Checkpoint 1 Worked-out solution availlable at...Ch. 2.2 - Checkpoint 2 Worked-out solution available at...Ch. 2.2 - Checkpoint 3 Worked-out solution available at...Ch. 2.2 - Checkpoint 5 Worked-out solution available at...Ch. 2.2 - Checkpoint 6 Worked-out solution available at...Ch. 2.2 - Checkpoint 7 Worked-out solution available at...Ch. 2.2 - Checkpoint 8 Worked-out solution available at...Ch. 2.2 - Checkpoint 9 Worked-out solution available at...Ch. 2.2 - Checkpoint 10 Worked-out solution available at...Ch. 2.2 - Checkpoint 11 Worked-out solution available at...Ch. 2.2 - In Exercises 1 and 2, evaluate each expression...Ch. 2.2 - In Exercises 1 and 2, evaluate each expression...Ch. 2.2 - In Exercises 3-6, simplify the expression....Ch. 2.2 - In Exercises 3-6, simplify the expression....Ch. 2.2 - In Exercises 3-6, simplify the expression....Ch. 2.2 - In Exercises 3-6, simplify the expression....Ch. 2.2 - 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In Exercises 1-10, simplify the expression....Ch. 2.4 - In Exercises 1114, f(2). 11.f(x)=3x2x+4Ch. 2.4 - In Exercises 1114, find f(2). 12.f(x)=x3+x2+8xCh. 2.4 - In Exercises 11-14, find f(2). 13.f(x)=27xCh. 2.4 - Using Relationships In Exercises 73-76, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Product Rule In Exercises 1-10, use the...Ch. 2.4 - Using the Quotient Rule In Exercises 11-20, use...Ch. 2.4 - Using the Quotient Rule In Exercises 11-20, use...Ch. 2.4 - 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Checkpoint 6 Worked-out solution available at...Ch. 2.5 - Checkpoint 7 Worked-out solution available at...Ch. 2.5 - Checkpoint 8 Worked-out solution available at...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 1-6, rewrite the expression with...Ch. 2.5 - In Exercises 7-10, factor the expression....Ch. 2.5 - In Exercises 7-10, factor the expression. 5xxx5x+1Ch. 2.5 - In Exercises 7-10, factor the expression....Ch. 2.5 - In Exercises 7-10, factor the expression....Ch. 2.5 - Decomposing Composite Functions In Exercises 1-6,...Ch. 2.5 - Decomposing Composite Functions In Exercises 1-6,...Ch. 2.5 - Decomposing Composite Functions In Exercises 1-6,...Ch. 2.5 - Decomposing Composite Functions In Exercises 1-6,...Ch. 2.5 - Decomposing Composite Functions In Exercises 1-6,...Ch. 2.5 - 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Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an equation of a Tangent Line In Exercises...Ch. 2.5 - Finding an equation of a Tangent Line In Exercises...Ch. 2.5 - Finding Horizontal Tangent Lines In Exercises...Ch. 2.5 - Finding Horizontal Tangent Lines In Exercises...Ch. 2.5 - Finding Horizontal Tangent Lines In Exercises...Ch. 2.5 - Finding Horizontal Tangent Lines In Exercises...Ch. 2.5 - Compound Interest You deposit $1000 in an account...Ch. 2.5 - Biology The number N of bacteria in a culture...Ch. 2.5 - Depreciation The value V of a machine t years...Ch. 2.5 - HOW DO YOU SEE IT? The cost C (In dollars) of...Ch. 2.5 - Credit Card Rate The average annual rate r (in...Ch. 2.6 - Checkpoint 1 Worked-out solution available at...Ch. 2.6 - Checkpoint 2 Worked-out solution available at...Ch. 2.6 - Checkpoint 3 Worked-out solution available at...Ch. 2.6 - Checkpoint 4 Worked-out solution available at...Ch. 2.6 - Checkpoint 5 Worked-out solution available at...Ch. 2.6 - Checkpoint 6 Worked-out solution available at...Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+292=0Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+88t=0Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2(2x+7)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=(x2+3x)(2x25)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x22x+7Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2+3x2x25Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Velocity and Acceleration A ball is propelled...Ch. 2.6 - Velocity and Acceleration A brick becomes...Ch. 2.6 - Velocity and Acceleration The velocity v (in feet...Ch. 2.6 - Stopping Distance A car is traveling at a rate of...Ch. 2.6 - Derivatives of Polynomial Functions Consider the...Ch. 2.6 - HOW DO YOU SEE IT? The graph shows the position,...Ch. 2.6 - Modeling Data The table shows the sales y (in...Ch. 2.6 - Finding a Pattern Develop a general rule for...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - Project: Cell Phone Subscribers in U.S. For a...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - Checkpoint 5 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Production Let x represent the units of labor and...Ch. 2.7 - HOW DO YOU SEE IT? The graph shows the demand...Ch. 2.7 - Health: U.S. Chickenpox Decline The numbers (in...Ch. 2.8 - Checkpoint 1 Worked-out solution available at...Ch. 2.8 - Checkpoint 2 Worked-out solution available at...Ch. 2.8 - Checkpoint 3 Worked-out solution available at...Ch. 2.8 - Checkpoint 4 Worked-out solution available at...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Area The radius r of a circle is increasing at a...Ch. 2.8 - Volume The radius r of a sphere is increasing at a...Ch. 2.8 - Area Let A be the area of a circle of radius r...Ch. 2.8 - Volume Let V be the volume of a sphere of radius r...Ch. 2.8 - Volume A spherical balloon is inflated with gas at...Ch. 2.8 - Volume The radius r of a right circular cone is...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Revenue The revenue R from selling x units of a...Ch. 2.8 - Profit The profit P from selling x units of a...Ch. 2.8 - Volume All edges of a cube are expanding at a rate...Ch. 2.8 - Surface Area All edges of a cube are expanding at...Ch. 2.8 - Boating A boat is pulled by a winch on a dock, and...Ch. 2.8 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.8 - Air traffic Control An airplane flying at an...Ch. 2.8 - Baseball A (square) baseball diamond has sides...Ch. 2.8 - Air Traffic Control An air traffic controller...Ch. 2.8 - Advertising Costs A retail sporting goods store...Ch. 2.8 - Environment An accident at an oil drilling...Ch. 2.8 - Profit A company is increasing the production of a...Ch. 2.8 - Sales The profit for a product is increasing at a...Ch. 2.8 - HOW DO YOU SEE IT? 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Finding Rates of Change In Exercises 5154, find...Ch. 2 - Finding Rates of Change In Exercises 5154, find...Ch. 2 - Velocity The height s (in feet) at time t (in...Ch. 2 - Velocity A rock is dropped from a tower on the...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit The profit P (in dollars) from...Ch. 2 - Population Growth The population P (in millions)...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - 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Solve each equation and check: 2(b+4)3=15

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Using Table 11-1, calculate the compound amount and compound interest for the following investment.
Principal ...

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Multiply. Leave all answers in trigonometric form. 5(cos15+isin15)2(cos25+isin25)

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In Exercises 19 to 24, classify each statement as true or false. Rain is wet or snow is cold.

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Determine whether each triple (a,b,c) is a Pythagorean triple. a)(3,4,5)c)(5,12,13)b)(4,5,6)d)(6,13,15)

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Let E and F be events such that FE. Find P(EF), and interpret your result.

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding Volume In Exercises 21-26, use a double integral to find the volume of the indicated solid.

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The area of the region bounded by , , and r = sec θ is:

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The mass of a thin wire shaped like the curve y = x2 from (0, 0) to (1, 1) with density at (x, y) is:

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Solve each formula for the indicated variable. x2a2y2b2=1; b

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Suppose that R2 = 0.723 for the model containing predictors x1,x4,x5, and x8 and R2 = 0.689 for the model with ...

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Write a formal version of the algorithm you developed for exercise 87.

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46. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
Compute the pro...

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