   Chapter 4.1, Problem 36E ### 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 the critical numbers of the function. h ( p ) = p − 1 p 2 + 4

To determine

To find: The critical number of the function h(p)=p1p2+4 .

Explanation

Definition used:

A critical number of a function f is a number c, if it satisfies either of the below conditions:

(1) f(c)=0

(2) f(c) does not exist.

Quotient Rule:

If two functions g(x) and h(x) are differentiable and h(x)0 , then the derivative of f(x)=g(x)h(x) is,

f(x)=h(x)g(x)g(x)h(x)[h(x)]2 (1)

Calculation:

Obtain the first derivative of the given function.

h(p)=ddp(p1p2+4)

Apply the Quotient rule as shown in equation (1),

h(p)=(p2+4)(1)(p1)(2p)(p2+4)2=p2+42p2+2p(p2+4)2=p2+2p+

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