Posted by **Tina** on Friday, November 26, 2010 at 5:51pm.

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

f(θ) = 2cos(θ) + (sin(θ))^2

- Calculus -
**Reiny**, Friday, November 26, 2010 at 10:49pm
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 -
**Anonymous**, Friday, October 26, 2012 at 9:44am
2sinθcosθ-1=0

## Answer This Question

## Related Questions

- Critical Numbers - 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 ...
- Pre Calculus - sec x = -2 , π ≤ x ≤ 3π Use a calculator to...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trigonometry - 5. If cot 2θ = 5/12 with 0 ≤ 2θ ≤ π...
- Trigonometry - if cot 2θ = 5/12 with 0≤2θ≤π find cos...
- Calculus - Compute, in terms of A, B, h, and k, the area enclosed by the curve ...
- trig - find cos(θ)ˏsin(θ)ˏtan(θ), if cot (2θ)=5/12...
- trigonometry - if cosθ=2/3 and tanθ<0 find the exact value sin(&#...
- math - if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5&#...

More Related Questions