Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.)

f(θ) = 4 cos θ + 2 sin^2 θ

1 answer

f = 4cosθ + 2sin^2θ
= 4cosθ + 2 - 2cos^2θ
f' = -4sinθ + 4cosθsinθ
critical numbers are when f'=0, so

4sinθ(cosθ-1) = 0
so, sinθ=0 or cosθ=1
...