Q:

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (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.) Need Help? Read It Watch It

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A:
Answer: f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2πWe plot the function using a graphing calculator (See attached image below)a) 1. Find the interval on which f is increasing. f(x) increases forx ∈ [π/2 , 7π/6] ∪ [3π/2, 11π/6]2. Find the interval on which f is decreasingf(x) decreases forx ∈ [0 , π/2) ∪ (7π/6, 3π/2) ∪ (11π/6, 2π](b) Find the local minimum and maximum values of fLocal minimum.      f = -9Local maximum.      f = 4.5(c) 1. Find the inflection pointsPlease see second image attachedPoints, (x,y) = (2.50673, -2.66882)(x,y) = (4.14456, 3.79382)(x,y) = (5.28022, 3.79382)2. Find the interval on which f is concave up.x ∈ [0 , 2.50673] ∪ [4.14456, 5.28022] 3. Find the interval on which f is concave down.x ∈ (2.50673, 4.14456) ∪ (5.28022, 2π]