Let f(x) = COS (ax) on the interval [3pi / 2a, 7pi / 2a]. where a > 0. List crit

Question

Let f(x) = COS (ax) on the interval [3pi / 2a, 7pi / 2a]. where a > 0. List critical points in order from smallest (A) to largest (B). A: B: For what x is f?(x) = 0 on (3pi / 2a, 7pi / 2a)? Call this point C. C: Indicate if the function is increasing (INC) or decreasing (DEC) on the following intervals: (3pi / 2a, A) (A, B): (B, 7pi / 2a) Indicate if the function is concave up (CU) or concave down (CD) on the following intervals: (3pi / 2a, C) (C, 7pi / 2a) Is point C an inflection point? (YES/NO)

Explanation / Answer

f'x = -asinax
f"x =-a^2cosax

critical point at -a^2cosax = 0
or ax = (2n+1)/2    n = integer

x = a/2 , 3a/2

for f'x >0 its increasing and for f'x<0 its decreasing

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