Question #753ef

1 Answer
Jan 25, 2018

They alternate between (local) maxes and (local) mins.

Explanation:

Let f(x) = 3cosx.
Then f is differentiable everywhere and
f'(x) = -3sinx.
f'(x) = 0 when sinx = 0; that is,
for all integer multiples of pi.
Now find f"(x).
You will discover from the Second Derivative Test that
when x is an even multiple of pi, f'(x) = 0 and f''(x) < 0.
Therefore f is concave down at such points and f has a local maximum.
Similarly, when x is an odd multiple of pi, f'(x) = 0 and f''(x) > 0.
Therefore f is concave up at such points and f has a local minimum.