Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 4.2, Problem 5PT
To determine
To choose: The appropriate option to complete the statement “if
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Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 4 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 4.1 - Prob. 1PTCh. 4.1 - Sometimes, Always, or Never: If f(c) = 0, then c...Ch. 4.1 - The critical numbers of f(x) = 3x4 = 20x3 36x2...Ch. 4.1 - Prob. 4PTCh. 4.1 - True or False: The absolute extrema of a...Ch. 4.1 - Prob. 6PTCh. 4.1 - Prob. 7PTCh. 4.2 - Prob. 1PTCh. 4.2 - Prob. 2PTCh. 4.2 - Prob. 3PT
Ch. 4.2 - True or False: If f(x) = g(x) for all x then f(x)...Ch. 4.2 - Prob. 5PTCh. 4.3 - Prob. 1PTCh. 4.3 - Prob. 2PTCh. 4.3 - Prob. 3PTCh. 4.3 - Prob. 4PTCh. 4.3 - Prob. 5PTCh. 4.3 - Prob. 6PTCh. 4.3 - True or False: If f(c) = 0, then c is a point of...Ch. 4.3 - Prob. 8PTCh. 4.3 - Prob. 9PTCh. 4.3 - Prob. 10PTCh. 4.4 - Prob. 1PTCh. 4.4 - Prob. 2PTCh. 4.4 - Prob. 3PTCh. 4.4 - limx(lnx)1/x= a) 0 b) 1 c) e d)Ch. 4.5 - Prob. 1PTCh. 4.5 - Prob. 2PTCh. 4.5 - Prob. 3PTCh. 4.5 - True or False: If f(x) 0 for all x in an interval...Ch. 4.5 - Prob. 5PTCh. 4.5 - Prob. 6PTCh. 4.5 - Prob. 7PTCh. 4.6 - Prob. 1PTCh. 4.6 - Prob. 2PTCh. 4.6 - Prob. 3PTCh. 4.7 - Prob. 1PTCh. 4.7 - A carpenter has a 10-foot-long board to mark off a...Ch. 4.7 - Prob. 3PTCh. 4.7 - Prob. 4PTCh. 4.8 - Prob. 1PTCh. 4.8 - Prob. 2PTCh. 4.8 - Prob. 3PTCh. 4.9 - Prob. 1PTCh. 4.9 - Prob. 2PTCh. 4.9 - Prob. 3PTCh. 4.9 - Prob. 4PTCh. 4.9 - Prob. 5PT
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