Math homework help

Question

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(theta)= 6 cos (theta) + 3 sin^2 (theta)

Answer 1

f(θ)=6cos(θ)+3sin²(θ)

f'(θ)=-6sin(θ)+6sin(θ)cos(θ)

sin(θ)(-1+cos(θ))=0

sin(θ) = 0 ==> sin^-1(0) = nπ

cos(θ) - 1 =0 ==> cos^-1(1) = 2nπ