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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find f'(a).

f(t) = 2t3 + t

To determine

To find: The derivative of the function f(t)=2t3+t at t=a.

Explanation

Formula used:

The derivative of a function f at a number a, denoted by f(a) is,

f(a)=limh0f(a+h)f(a)h (1)

Calculation:

Obtain the derivative of the function f(t) at t=a.

Compute f(a) by using the equation (1).

f(a)=limh0f(a+h)f(a)h=limh0(2(a+h)3+(a+h))(2(a)3+(a))h=limh0(2(a3+3a2h+3ah2+h3)+(a+h))(2a3+a)h=limh0(2a3+6a2h+6ah2+3h3+(a+h)

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