## Analysis of the Function \( f(x) = 3 \sin x + 3 \cos x \) on \((-π, π)\)### a) Determine the Intervals of Concavity- **Intervals where \( f \) is concave up:** \[ (-π, -π/4) \cup (3π/4, π) \]- **Intervals where \( f \) is concave down:** \[ (-π/4, 3π/4) \]### b) Inflection PointsBased on the concavity intervals determined in part (a), identify the inflection points of the function \( f \). Each inflection point should be entered as an ordered pair \((x, y)\).- Inflection points: \[ (-π/4, 0), (3π/4, 0) \]### c) Critical Numbers and Relative ExtremaUse the second derivative test to determine the relative extrema of the function \( f \). List only the x-coordinates.- **Relative maxima at:** \[ \frac{π}{4} \]- **Relative minima at:** \[ -\frac{3π}{4} \]### d) Relative Extremum of \( f' (x) \)Find the x-values where \( f'(x) \) has a relative maximum or minimum.- **\( f'(x)\) has a relative maxima at:** \[ (input box) \]- **\( f'(x)\) has a relative minima at:** \[ (input box) \]

f(z) = 3 sin z+3 cos z, on (-x, x) ODetermine the intervals on which f is concave up and concave down. is concave up on: (-pi,-pi/4)U(3pi/4,pi) !! is concave down on: (-pi/4,3pi/4) !! O 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 (, y). (-pi/4,0).(3pi/4,0) !! (Separate multiple answers by commas.) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the r-coordinates. telative maxima at: pi/4 !! (Separate multiple answers by commas.) Lelative minima at -3pi/4 (Separate multiple answers by commas.) ) Find the r-value(s) where f'(r) has a relative maximum or minimum. has relative maxima at: (Separate multiple answers by commas.) has relative minima at (Separate multiple answers by commas.)

f(z) = 3 sin z+3 cos z, on (-x, x) ODetermine the intervals on which f is concave up and concave down. is concave up on: (-pi,-pi/4)U(3pi/4,pi) !! is concave down on: (-pi/4,3pi/4) !! O 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 (, y). (-pi/4,0).(3pi/4,0) !! (Separate multiple answers by commas.) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the r-coordinates. telative maxima at: pi/4 !! (Separate multiple answers by commas.) Lelative minima at -3pi/4 (Separate multiple answers by commas.) ) Find the r-value(s) where f'(r) has a relative maximum or minimum. has relative maxima at: (Separate multiple answers by commas.) 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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