This is an ungraded practice free response question! (2, 1)1+Graph of f1- 2 In (2-), -5 sxs2g(x), 2

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(2, 1) Graph of f The derivative of a function fis defined by f'(x) =/1-2 in (2-), -5≤x≤2 where the graph of g is a g(x), 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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This is an ungraded practice free response question!

(2, 1)
1+
Graph of f
1- 2 In (2-), -5 sxs2
g(x), 2<xs5
The derivative of a function fis defined by f '(x) = -
where the graph of g is a
line segment. The graph of the continuous function f' is shown in the figure above. Let f(3) = 4.
a) Find the x-coordinate of each critical point of f and classify each as the location of a relative
minimum, a relative maximum, or neither a minimum nor a maximum. Justify your answer.
b) Determine the absolute maximum value of f on the closed interval -5 sxs 5. Justify your answer.
c) Find the x-coordinates of all points of inflection of the graph of f. Justify your answer.
d) Determine the average rate of change of f' over the interval -3 sxs3. Does the mean value
theorem guarantee a value of c for -3 <c <3 such that f" is equal to this average rate of
change? Justify your answer.

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