Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Consider the equation below. (If an answer does not exist, enter DNE.)** \( f(x) = 3 \sin(x) + 3 \cos(x), \quad 0 \leq x \leq 2\pi \) ### (a) Find the interval on which \( f \) is increasing. (Enter your answer using interval notation.) \( \left(0, \frac{\pi}{4}\right) \cup \left(\frac{5\pi}{4}, 2\pi\right) \) (✓) **Find the interval on which \( f \) is decreasing. (Enter your answer using interval notation.)** \( \left(\frac{\pi}{4}, \frac{5\pi}{4}\right) \) (✓) ### (b) Find the local minimum and maximum values of \( f \). - **Local minimum value**: \( \frac{5\pi}{4}, -3\sqrt{2} \) (✗) - **Local maximum value**: \( \frac{\pi}{4}, 3\sqrt{2} \) ### (c) Find the inflection points. - \( (x, y) = \) [ ] (smaller x-value) - \( (x, y) = \) [ ] (larger x-value) **Find the interval on which \( f \) is concave up. (Enter your answer using interval notation.)** - [ ] **Find the interval on which \( f \) is concave down. (Enter your answer using interval notation.)** - [ ]
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Transcribed Image Text:**Consider the equation below. (If an answer does not exist, enter DNE.)** \( f(x) = 3 \sin(x) + 3 \cos(x), \quad 0 \leq x \leq 2\pi \) ### (a) Find the interval on which \( f \) is increasing. (Enter your answer using interval notation.) \( \left(0, \frac{\pi}{4}\right) \cup \left(\frac{5\pi}{4}, 2\pi\right) \) (✓) **Find the interval on which \( f \) is decreasing. (Enter your answer using interval notation.)** \( \left(\frac{\pi}{4}, \frac{5\pi}{4}\right) \) (✓) ### (b) Find the local minimum and maximum values of \( f \). - **Local minimum value**: \( \frac{5\pi}{4}, -3\sqrt{2} \) (✗) - **Local maximum value**: \( \frac{\pi}{4}, 3\sqrt{2} \) ### (c) Find the inflection points. - \( (x, y) = \) [ ] (smaller x-value) - \( (x, y) = \) [ ] (larger x-value) **Find the interval on which \( f \) is concave up. (Enter your answer using interval notation.)** - [ ] **Find the interval on which \( f \) is concave down. (Enter your answer using interval notation.)** - [ ]
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