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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9.6, Problem 31E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 29 and 30, complete the following for each function.

(a) Find f'(x).

(b) Check your result in part (a) by graphing both it and the numerical derivative of the function.

(c) Find x-values for which the slope of the tangent is 0.

(d) Find points (x, y) where the slope of the tangent is 0.

(e) Use a graphing utility to graph the function and locate the points found in part (d).

f ( x ) = ( x 2 − 4 ) 3 + 12

(a)

To determine

To calculate: The derivative f′(x) of the function f(x)=(x2−4)3+12.

Explanation

Given Information:

The function is f(x)=(x2−4)3+12.

Formula used:

According to the power rule, if f(x)=xn, then,

f′(x)=nxn−1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g′(x)=cf′(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f′(x)=u′(x)+v′(x)

According to the product rule, if f(x)=u(x)â‹…v(x), then

f′(x)=u′(x)⋅v(x)+v′(x)⋅u(x)

According to the property of differentiation, if a function is of the form y=un, where u=g(x),

dydx=nun−1dudx

Calculation:

Consider the provided function,

f(x)=(x2−4)3+12

Consider (x2−4) to be u,

f(x)=u3+12

Differentiate both sides with respect to x,

f′(

(b)

To determine

To graph: The derivative f′(x) of the function f(x)=(x2−4)3+12 and the numerical derivative of the function to check the results in part (a).

(c)

To determine

To calculate: The x-values for which the slope of the tangent of the function f(x)=(x2−4)3+12 is 0.

(d)

To determine

To calculate: The points (x,y) where the slope of the tangent of the function f(x)=(x2−4)3+12 is 0.

(e)

To determine

To graph: The function f(x)=(x2−4)3+12 and locate the points for which the slope of the tangent of the function is 0 using graphing utility.

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Sect-9.1 P-1CPSect-9.1 P-2CPSect-9.1 P-3CPSect-9.1 P-4CPSect-9.1 P-5CPSect-9.1 P-6CPSect-9.1 P-7CPSect-9.1 P-8CPSect-9.1 P-9CPSect-9.1 P-10CP
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Sketching a CurveShow that the vector-valued function r(t)=ti+2tcostj+2tsintk lies on the cone 4x2=y2+z2. Sketc...

Calculus (MindTap Course List)

Describe the relationship between the alpha level and the likelihood of making a Type I error.

Research Methods for the Behavioral Sciences (MindTap Course List)

A hypothesis test attempts to rule out chance, or sampling error, as a plausible explanation for the results fr...

Research Methods for the Behavioral Sciences (MindTap Course List)

Finding the Best Car Value When trying to decide what car to buy, real value is not necessarily determined by h...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Verifying Greens TheoremIn Exercises 58, verify Greens Theorem by evaluating both integrals cy2dx+x2dy=R(NxMy)d...

Multivariable Calculus

Determine whether the graph of each quadratic function opens upward or downward. State whether a maximum or min...

College Algebra (MindTap Course List)

The following table contains observed frequencies for a sample of 200. Test for independence of the row and col...

Statistics for Business & Economics, Revised (MindTap Course List)

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