10) The following problem uses techniques and formulas presented in Chapter 2.2 (Don't use the Limit process ) Find the slopes of the graph of f (2) = x³ at z = -1, 0, andi

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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10) The following problem uses techniques and formulas presented in Chapter 2.2 (Don't use the Limit process )
Find the slopes of the graph of f (2) = x³
at z = -1, 0, andi
Transcribed Image Text:10) The following problem uses techniques and formulas presented in Chapter 2.2 (Don't use the Limit process ) Find the slopes of the graph of f (2) = x³ at z = -1, 0, andi
Expert Solution
Step 1

Given the function

f(x) = x3

we need to find slopes of f(x) at x = -1 , 0 and 1.

Now, 

f(x) = x3

f'(x) = 3x2

Therefore slope of f(x) at different values of x are as follows

At x = -1 

f'(-1) = 3(-1)2

        = 3(1)

      = 3

So, slope of f(x) at x = -1 is 3.

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