6. 0/8 points Previous Answers SCalc8 3.3 014 Consider the equation below. (If a

Question

6. 0/8 points Previous Answers SCalc8 3.3 014 Consider the equation below. (If an answer does not exist, enter DNE) f(x) 3 cos2(x) 6 sin(x), 0SxS 2 (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 infiection points. (smaller x-value) x, y) (larger x-value Find the interval on which f is concave up. (Enter your answer using interval notation.) rind the interval on which f is concave down. (Enter your answer using interval notation.) Noed Help? Rasher do 4

Explanation / Answer

a)

f(x) = 3cos²x -6sinx

find deriavtive as

f'(x) = 6cosx(-sinx)-6cosx

To find critical point, solve f'(x) =0

-6cosx(sinx+1) =0

x =pi/2, 3pi/2

hence

a)

Increasing in (pi/2, 3pi/2)

Decreasing in (0, pi/2)U(3pi/2, 2pi)

b)

local minimum value is -6

local maximum is 6

c)

Inflection point is

(pi/6, -3/4)

(5pi/6, -3/4)

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Concave up in (pi/6, 5pi/6)

concave down in (0, pi/6)U(5pi/6, 3pi/2)U(3pi/2, 2pi)

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