   Chapter 5.2, Problem 48E ### 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 )   =  12 x 3 ( 3 x 4   –   2 ) 3 ;  ( 1 ,  -3 )

To determine

To calculate: The equation of the function f that has given derivative f(x)=12x3(3x42)3

And given point (1,3).

Explanation

Given Information:

The provided derivative is f(x)=12x3(3x42)3 and the provided point is (1,3).

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)=12x3(3x42)3.

It can be written as,

df(x)dx=12x3(3x42)3

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

f(x)=12x3(3x42)3dx …… (1)

Let 3x42.

Differentiate with respect to x,

ddx(3x42)=dudxddx(3x4)ddx(0)=dudx12x3=dudx12x3dx=du

Substitute the value of 12x3dx=du and 3x42=u in equation (1),

f(x)=u3du

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