Question

Find the critical numbers of the function on the interval 0 ≤ θ < 2π. Small & large value

f(θ) = 2cos(θ) + (sin(θ))^2

Answer 1

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

Answer 2

2sinθcosθ-1=0