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Calculus

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

f(θ) = 2cos(θ) + (sin(θ))^2

  • Calculus - ,

    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

  • Calculus - ,

    2sinθcosθ-1=0

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