   Chapter 4.1, Problem 33E ### 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.g(t) = t4 + t3 + t2 + 1

To determine

To find: The critical number of the function g(t)=t4+t3+t2+1 .

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.

Formula used:

The Power Rule:

If n is positive integer, then ddx(xn)=nxn1 . (1)

Calculation:

Obtain the first derivative of the given function.

g(t)=ddt(t4+t3+t2+1)=ddt(t4)+ddt(t3)+ddt(t2)+ddt(1)

Apply the power rule as shown in equation (1).

g(t)=(4t41)+(3t31)+(2t21)+0=4t3+3t2+2t

Take g(t)=0 to obtain the critical number

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