   Chapter 4.1, Problem 48E ### 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 absolute maximum and absolute minimum values of f on the given interval.f(x) = 5 + 54x − 2x3, [0, 4]

To determine

To find: The absolute maximum and absolute minimum of the given function.

Explanation

Given:

The function is f(x)=5+54x2x3 in the interval [0,4].

Formula used:

Power Rule:

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

Calculation:

Obtain the first derivative of the given function.

f(x)=ddx(5+54x2x3)

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

f(x)=ddx(5)+ddx(54x)ddx(2x3)=0+54(1)2(3x2)=546x2

Set f(x)=0 and obtain the critical numbers.

546x2=06(9x2)=09x2=0x2=9

Find the square root of x.

x=9x=±3

That is, x=3 and x=3

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