Posted by **Michael** on Saturday, December 4, 2010 at 4:16pm.

Find the critical numbers of the function on the interval 0 ≤ θ < 2π.

f(θ) = 2cos(θ) + (sin(θ))^2

- Critical Numbers -
**MathMate**, Saturday, December 4, 2010 at 7:06pm
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:

http://img256.imageshack.us/img256/11/1291497419.png

- Critical Numbers -
**Anonymous**, Sunday, November 30, 2014 at 9:05pm
solve on the interval of 0,2π, cos θ / 3 =-1

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