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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

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 ( t ) = t 1 + t 2 , [ 0 , 2 ]

To determine

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

Explanation

Given:

The function f(t)=t1+t2 in the interval [0,2].

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.

f(t)=ddt(t1+t2)

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

f(t)=(1+t2)(12(t)12)(2t)t(1+t2)2=(1+t2)(12t)(2t)t(1+t2)2

Multiply and divided by 2t,

f(t)=2t2t[(1+t2)(12t)(2t)t(1+t2)2]=(1+t2)2(2t)tt2t(1+t2)2=1+t24t22t(1+t2)2=13t22t(1+t2)2

Set f(t)=0 and obtain the critical numbers as follows

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