8. Question: If you know the point (5, –1) lies on the function and that the point (2,7) lies on the tangent line to the function at x = 5, then what is f'(5)? What type of behavior would the function have at x = 5?

Q: a. Find the function f given that the slope of the tangent line to the graph of f at any point…

A:

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: The tangent line to the graph of y = f(x) at the point (9, 20) has the equation y = 2x +2. (a) Find…

A: Use formula of instantaneous rate of change

Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

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Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: The tangent line to y=f(x) at (2,8) passes through the point (-6,-9). Compute the following. a.)…

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Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

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Q: 2. Use implicit differentiation to find tangent at the given point: (a) xy + y² = 3-3x² at (-1,1).…

A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

A:

Q: 4) Consider function sin(xy) =y a) Use implicit differentiation to find the derivative y'(x) at the…

A: sinxy=y a). Differentiating with respect to x, we get…

Q: Find an equation of the tangent line to the curve y = at the point (0, 5). + 1 y= 5x – 5

A: Given,            y =5exx2+1 and point (0,5)

Q: Compute central difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Central difference formula for derivative  f′(x)≈f(x+h)−f(x−h)2h.

Q: 6. Find 39th derivative of f(x) = sinh(x). A. sinh(x) B. cosh(x) C. – sinh(x) D. - cosh(x) None of…

A: Derivative of sinh(x) is Cosh(x) and  Derivative of Cosh(x) is Sinh(x).

Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: a. First compute the Derivative of f(x) = x and then use it to find the slope of the tangent line to…

A: Equation of Tangent to a curve: Let y=f(x) be the equation of a curve. Then the equation of tangent…

Q: Compute central difference approximations for the first derivative of the function, y = e'cos(x?),…

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Q: Find an equation of the tangent line to the graph of the function at the given point. You must write…

A: y=5coshx-sinhx2,   0,5let 'm' be slope of tangent line.m=dydx=10coshx-sinhxsinhx-coshx

Q: The implicit curve given by the equation x + xy + y= 1 has derivative dy 2x+ y %3D dx x + 2y Show…

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Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: Compute central difference approximations for the first derivative of the function, y = cos(sin(x)+…

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Q: 11) We defined derivatives using a secant line to estimate a tangent line. In the definition, what…

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Q: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: Question 1 Find the derivative of g(x) = 3 cos™' (x) at the point x = 4 %3D %3D (Enter an exact…

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Q: 4.) f (x) 3D х2 – 1

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Q: Let y = 5−2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to…

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Q: Find the equation of the tangent line to the curve when x has the given value.  1. f(x) = x2 -1;…

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Q: (# 11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) =…

A: For the equation of tangent, we need to find the slope of the function at x=1.

Q: 2 6. Consider f(x) x + 1 a. Find f'(x) using the formal definition of the derivative. b. Find the…

A: Solve the function

Q: 20 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph…

A: We have to find

Q: 3. Give the definition of a derivative of a function f of one variable at a point xo. /2 Find the…

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Q: 2 If f(x) find f'(3) and us it to find an equation of the tangent line to the curve y = at ズー1 ズ-1…

A: Given function is, fx=2x-1

Q: find the equation of tangent line of function f(x)=csc(x)-cos(x)1/2 at the point ((2*3.14)/3,…

A:

Q: 1.Find the derivative of the function y = cosh*x – sinh“ x - 2.Find the derivative of y = In cosh x.…

A: Q1)   Given  y= cosh4x -sinh4x         As per our guideline we supposed  to answer only first…

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

Q: 4) Suppose an object moves along a horizontal path with the position function x(f) = 4t – t2 on the…

A: Concept: Rate of change of position function at time (t०) gives velocity.  That is  Velocity…

Q: At what other point does the tangent line drawn to the curve f (x) = x ^ 3 from (2,8) intersect?

A: Given curve is : f(x)=x3   ..............(1)           and tangent drawn from (2,8)

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

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Q: 11. True or false: If the function f represents position (height or displacement), then the…

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Q: Compute central difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: here we will use central difference formula  f'x≈fx+∆x-fx-∆x2×∆x

Q: Use the graph of f'(x), the derivative of f(x), given to the right to answer the following question.…

A: Given that f(3)=-3 So, let x0=3⇒y0=f(x0)=f(3)=-3 And from the graph f'(3)=2⇒m=f'y0=2

Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)

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Q: Determine the location of any horizontal tangent lines to the graph of f ( x ) = cos ⁡ x − x on [ 0…

A: Given,          fx=cosx-x  on  [0,2π)

Q: 28. Use mplicit differentiation to find an equation of the tangent line to the curve at the given…

A: We know that the expression for the slope of the tangent to the curve is: m=dydx And  The expression…

Q: 2. Use the definition of the derivative to find the first and second derivatives of the function. 1…

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Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 1. State the power rule. 2. For which values of n have we proved the power rule? 3. Based on your…

A: 1. The power rule of derivatives gives the following: For any real number n,      ddxxn=nxn-1

Q: 10.(a) Find the derivative of the function f(x) =x² +2 using the definition of derivative. (b) What…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: