Calculus
posted by Tina on .
Find the critical numbers of the function on the interval 0 ≤ θ < 2π. Small & large value
f(θ) = 2cos(θ) + (sin(θ))^2

let's take f '(Ø)
f '(Ø) = 2sinØ + 2sinØcosØ
= 0 for max/mins
sinØ  sinØcosØ = 0
sinØ(1 + cosØ) = 0
sinØ = 0 or cosØ = 1
Ø = 0,π,2π or Ø = 3π/2
f(0) = 2+0 = 2
f(π) = 2+0 = 2
f(2π) = 2 + 0 = 2
f(3π/2) = 0 + 1 = 0
max value of the function is 2 when Ø = 0 or 2π
min value of the function is 2 when Ø = 3π/2 
2sinθcosθ1=0