   Chapter 5.2, Problem 49E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding an Equation of a Function In Exercises 47-50, find an equation of the function f that has the given derivative and whose graph passes through the given point. f ’ ( x )   =  2 x ( 4 x 2   –  10 ) 2 ;  ( 2 ,  10 )

To determine

To calculate: The equation of the function f that has given derivative f(x)=2x(4x210)2

And given point (2,10).

Explanation

Given Information:

The provided derivative is f(x)=2x(4x210)2 and the provided point is (2,10).

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

where n1

Calculation:

Consider the derivative f(x)=2x(4x210)2.

It can be written as,

df(x)dx=2x(4x210)2

Integrate df(x)dx to obtain f(x).

f(x)=2x(4x210)2dx …… (1)

Let 4x210=u.

Differentiate with respect to x,

ddx(4x210)=dudxddx(4x2)ddx(10)=dudx8x=dudx2xdx=du4

Substitute the value of 2xdx=du4 and 4x210=u in equation (1),

f(x)=u24du

Now, apply the general power rule for integrtion in the above equation

f(x)=<

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