# Calculus

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Consider the function f(x)=3cosx−cos^(3)x for 0<x<2π.

For the following questions, write inf for ∞, -inf for −∞, U for the union symbol, None if no answer exists, and separate by a comma if more than one answer exist.

a.) The x-intercepts are .

b.) f′(x)= .

c.) f(x) is increasing on the interval(s) .

d.) f(x) is decreasing on the interval(s) .

e.) f(x) has a local maximum at x = .

f.) f(x) has a local minimum at x = .

g.) f′′(x)= .

h.) f(x) is concave up on the interval(s) .

i.) f(x) is concave down on the interval(s) .

j.) The x-coordinate of the points of inflection are

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