   Chapter 3.1, Problem 41E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find f'(x). Compare the graphs of f and f' and use them to explain why your answer is reasonable.f(x) = x4 – 2x3 + x2

To determine

To find: The derivative of f(x). That is, f(x).

Explanation

Given:

The function f(x)=x42x3+x2.

Derivative rules:

(1) Constant Multiple Rule: ddx[cf(x)]=cddxf(x)

(2) Power Rule: ddx(xn)=nxn1

(3) Sum Rule: ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x))

(4) Difference Rule: ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

Calculation:

The derivative of f(x) is f(x), which is obtained as follows,

f(x)=ddx(f(x)) =ddx(x42x3+x2)

Apply the sum rule (3),

f(x)=ddx(x42x3)+ddx(x2)

Apply the difference rule (4),

f(x)=ddx(x4)ddx(2x3)+ddx(x2)

Apply the constant multiple rule (1),

f(x)=ddx

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