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) = 10 cos(θ) + 5 sin2(θ)

The critical numbers of the function will be at ()

Given the function

f(θ) = 10 cos(θ) + 5 sin2(θ)

At the turning point,

At the turning point,

Hence critical numbers of the function will be at ()

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If

then the derivative is

Critical points occur where . This happens for

In the first case, we find

In the second,

So all the critical points occur at multiples of , or . (This includes all the even multiples of .)

stops on an even number.