NOTE: When using interval notation in WeBWorKk, remember that: You use 'INF' for o and '-INF' for -oo. And use 'U' for the union symbol. Enter DNE if an answer does not exist. f(x) = 2 sin x + 3 cos x, on (-x, R) a) Determine the intervals on which f is concave up and concave down. f is concave up on: f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x, y)). (Separate multiple answers by commas.) c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at: (Separate multiple answers by commas.) Relative minima at: (Separate multiple answers by commas.) d) Find the x-value(s) where f'(x) has a relative maximum or minimum. f' has relative maxima at: (Separate multiple answers by commas.) f' has relative minima at: (Separate multiple answers by commas.)

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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NOTE: When using interval notation in WeBWork, remember that:
You use 'INF' for o and '-INF' for -oo.
And use 'U' for the union symbol.
Enter DNE if an answer does not exist.
f(x) = 2 sin x + 3 cos x,
on (-x, x)
a) Determine the intervals on which f is concave up and concave down.
f is concave up on:
f is concave down on:
b) Based on your answer to part (a), determine the inflection points of f. Each point
should be entered as an ordered pair (that is, in the form (x, y)).
(Separate multiple answers by commas.)
c) Find the critical numbers of f and use the Second Derivative Test, when possible,
to determine the relative extrema. List only the x-coordinates.
Relative maxima at:
(Separate multiple answers by
commas.)
Relative minima at:
(Separate multiple answers by
commas.)
d) Find the x-value(s) where f'(x) has a relative maximum or minimum.
f' has relative maxima at:
(Separate multiple
answers by commas.)
f' has relative minima at:
(Separate multiple
answers by commas.)
Transcribed Image Text:NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for o and '-INF' for -oo. And use 'U' for the union symbol. Enter DNE if an answer does not exist. f(x) = 2 sin x + 3 cos x, on (-x, x) a) Determine the intervals on which f is concave up and concave down. f is concave up on: f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x, y)). (Separate multiple answers by commas.) c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at: (Separate multiple answers by commas.) Relative minima at: (Separate multiple answers by commas.) d) Find the x-value(s) where f'(x) has a relative maximum or minimum. f' has relative maxima at: (Separate multiple answers by commas.) f' has relative minima at: (Separate multiple answers by commas.)
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