Critical Numbers

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Find the critical numbers of the function on the interval 0 ≤ θ < 2π.
f(θ) = 2cos(θ) + (sin(θ))^2

  • Critical Numbers -

    Critical point:
    A critical point at the interior of the domain of a function is the point where the derivative is zero or undefined.

    f(θ) = 2cos(θ) + (sin(θ))^2
    does not have any undefined points for θ∈ℝ.
    So we only need to find the values of θ which make f'(θ)=0.
    Differentiate f(θ) and equate to zero. Solve for all roots for the equation and these are the critical points.

    The following graph might help you check you answer:

  • Critical Numbers -

    solve on the interval of 0,2π, cos θ / 3 =-1

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