(a) Find the interval on which f is increasing. (Enter your answer using interval notation.) π 3π 2' 2 Find the interval on which f is decreasing. (Enter your answer using interval notation.) (0, 2) U ( 321,2π) (b) Find the local minimum and maximum values of f. -18 local minimum value local maximum value (c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.) 9 4 (x, y) = (x, y) = π 6' 18 5π 207 6' 4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.5: Product-to-sum And Sum-to-product Formulas
Problem 40E
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Question
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = 9 cos²(x) — 18 sin(x), 0 ≤ x ≤ 2π
(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)
π 3π
2' 2
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
3π
2
π
0,72
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(x, y)
,27
=
(c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.)
9
(x, y) = (
π
6'
-
-18
5π 207
6⁹ 4
18
X
Transcribed Image Text:Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 9 cos²(x) — 18 sin(x), 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) π 3π 2' 2 Find the interval on which f is decreasing. (Enter your answer using interval notation.) 3π 2 π 0,72 (b) Find the local minimum and maximum values of f. local minimum value local maximum value (x, y) ,27 = (c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.) 9 (x, y) = ( π 6' - -18 5π 207 6⁹ 4 18 X
Expert Solution
Step 1

The given function is:

fx=9 cos2x-18 sinx,  0x2π

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