   Chapter 5.3, Problem 50E ### 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 ) = x 3 − 4 x 2 + 3 x − 3 ;   ( 4 ,   − 1 )

To determine

To calculate: The equation of function f(x) that has derivative f(x)=x34x+3x3 and whose graph passes through the point (4,1).

Explanation

Given Information:

The first derivative f(x)=x34x+3x3.

The coordinate of point (4,1).

Formula used:

The general exponent rule of integrals:

eu(x)du(x)=ln|u(x)|+C

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider the derivative:

f(x)=x34x+3x3

Rewrite the integrand as:

df(x)dx=x34x+3x3

Apply, integration on both sides:

df(x)dxdx=x34x+3x3dx+Cf(x)=(x2x36x3)dx+Cf(x)=(x2)dx+(x)dx+Ȣ

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