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f(x) — 3 sin х + 3 сos x, on (- π, π) a) Determine the intervals on which f is concave up and concave down. f is concave up on: (-pi,-pi/4) U (3pi/4,pi) ... f is concave down on: (-pi/4,3pi/4) ... ... 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)). ... (-pi/4,0),(3pi/4,0) (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: pi/4 (Separate multiple answers by commas.) Relative minima at: -3pi/4 (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: ... pi/4 (Separate multiple answers by commas.) f' has relative minima at: 5pi/4 (Separate multiple answers by commas.)

f(x) — 3 sin х + 3 сos x, on (- π, π) a) Determine the intervals on which f is concave up and concave down. f is concave up on: (-pi,-pi/4) U (3pi/4,pi) ... f is concave down on: (-pi/4,3pi/4) ... ... 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)). ... (-pi/4,0),(3pi/4,0) (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: pi/4 (Separate multiple answers by commas.) Relative minima at: -3pi/4 (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: ... pi/4 (Separate multiple answers by commas.) f' has relative minima at: 5pi/4 (Separate multiple answers by commas.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 32E
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I DID THIS, I JUST GOT LAST 2 WRONG. PLSS HELP

f(x) — 3 sin х + 3 сos x, on (- π, π) a) Determine the intervals on which f is concave up and concave down. f is concave up on: (-pi,-pi/4) U (3pi/4,pi) ... f is concave down on: (-pi/4,3pi/4) ... ... 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)). ... (-pi/4,0),(3pi/4,0) (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: pi/4 (Separate multiple answers by commas.) Relative minima at: -3pi/4 (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: pi/4 (Separate multiple answers by commas.) f' has relative minima at: 5pi/4 (Separate multiple answers by commas.)
Transcribed Image Text:f(x) — 3 sin х + 3 сos x, on (- π, π) a) Determine the intervals on which f is concave up and concave down. f is concave up on: (-pi,-pi/4) U (3pi/4,pi) ... f is concave down on: (-pi/4,3pi/4) ... ... 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)). ... (-pi/4,0),(3pi/4,0) (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: pi/4 (Separate multiple answers by commas.) Relative minima at: -3pi/4 (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: pi/4 (Separate multiple answers by commas.) f' has relative minima at: 5pi/4 (Separate multiple answers by commas.)
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