finding critical points?

Question

Hi, I need urgent help finding critical numbers of the function on the interval 0 ≤ θ < 2pi. f(θ) = 2cos(θ) + sin^2(θ).

Any help would be appreciated!

how would I find the max and min

Answer 1

a critical number is a number where the value of the derivative is zero.

so we have to compute the derivative of the function and solve it for zero value.

f ' (theta) = -2sin(theta) + 2sin(theta)cos(theta) = 0

theta = 0, pi and 2pi.

So critical numbers would be 0, pi, and 2pi

Answer 2

don't know if I'm entitled to any points for such an answer but don't you find the double derivative where it = 0 for critical points...you prob. know that and need help with the actual working out...