Question

Only g and h needs answers

(1 point) Book Problem 3 Consider the function f(x) = x + 2 cos(x), 0<x<21. For the following questions, write inf for , -inf for - , U for the union symbol, and NA (ie. not applicable) if no such answer exists. a.) f'(x) = 1-2sinx b.) f(x) is increasing on the interval(s) (0,pi/6)U(5pi/6,2pi) c.) f(x) is decreasing on the interval(s) (pi/6,5pi/6) d.) f(x) has a local minimum at 5pi/6 e.) f(x) has a local maximum at pi/6 f.) f'(x) = -2cosx g.) f(x) is concave up on the interval(s) (0,pi/2)U(3pi/2,2pi) h.) f(x) is concave down on the interval(s) (pi/2,3pi/2) 1.) f(x) has 2 points of inflection at A = pi/2 and B = 3pi/2 where A<B.

Answer 1

f(x) = x+2cos(x)

f'(x) = 1-2sin(x)

f"(x) = -2sin(x)cos(x)

= -sin2x

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