The graphs of the function and its derivative are shown above for -1≤x≤4 . (a) Find the average rate of change of f over the interval -1≤x≤4. For how many values of x in the interval -1≤x≤4 does the instantaneous rate of change of f equal the average rate of change of f over that interval? (b) Write an equation for the line tangent to the graph of f at x = 1 (c) For each of lim x→2 (f(x)−f(2))/x−2 and lim x→3 (f(x)−f(3))/x−3, find the value or give a reason why it does not exist.
The graphs of the function and its derivative are shown above for -1≤x≤4 . (a) Find the average rate of change of f over the interval -1≤x≤4. For how many values of x in the interval -1≤x≤4 does the instantaneous rate of change of f equal the average rate of change of f over that interval? (b) Write an equation for the line tangent to the graph of f at x = 1 (c) For each of lim x→2 (f(x)−f(2))/x−2 and lim x→3 (f(x)−f(3))/x−3, find the value or give a reason why it does not exist.
Calculus: Early Transcendentals
8th Edition
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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The graphs of the function and its derivative are shown above for -1≤x≤4 .
(a) Find the average rate of change of f over the interval -1≤x≤4. For how many values of x in the interval -1≤x≤4 does the instantaneous rate of change of f equal the average rate of change of f over that interval?
(b) Write an equation for the line tangent to the graph of f at x = 1
(c) For each of lim x→2 (f(x)−f(2))/x−2 and lim x→3 (f(x)−f(3))/x−3, find the value or give a reason why it does not exist.
(d) Let g be the function defined by g(x)=e^xf(x). Find g′(0).
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Graph of f
3
4
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6
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Graph of f'
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