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

## Answer This Question

## Related Questions

- Calculus - Find the critical numbers of the function on the interval 0 ≤...
- Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...
- Math - Find the critical numbers of the functions: F(x) = x^(4/5)(x-4)^2 f(θ...
- Math - Calculus - The identity below is significant because it relates 3 ...
- Pre Calculus - sec x = -2 , π ≤ x ≤ 3π Use a calculator to...
- Trigonometry - if cot 2θ = 5/12 with 0≤2θ≤π find cos...
- trig - find cos(θ)ˏsin(θ)ˏtan(θ), if cot (2θ)=5/12...
- Algebra - What values for θ (0≤θ≤2π) satisfy the ...
- PreCalc - I'm not sure how to solve these with calculator. sec x = -2 , π...
- trigonometry - 5. If cot 2θ = 5/12 with 0 ≤ 2θ ≤ π...

More Related Questions