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Q21.

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Precalculus Mathematics for Calculus
Found in: Page 922
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Find the derivative of the function at the given number.

f(x)=x3x2, at 1.

The derivative of the function at 1is7.

See the step by step solution

Step by Step Solution

Step 1. Given information.

The function here given is,

f(x)=x3x2, at 1

Step 2. Formula used.

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

.f'(a)=limh0f(a+h)f(a)h

if this limit exists.

Step 3. Finding the slope of the tangent line at a given point.

According to the definition of a derivative, with,a=1 we have

f'(1)=limh0f(1+h)f(1)h Definition of f'(1)=limh0[(1+h)3(1+h)2][13(1)2]h f(x)=x3x2=limh0[1+h3(1+h22h)]+4h Expand=limh01+h33h2+6h+4h=limh03h2+7hh Simplify=limh0(3h+7) Cancel h=7

Therefore, the derivative of the function at 1is7 .

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