Find the critical numbers of f(t) = sin^2 t - cos t

Question

cruffo · Answer

What steps are involved in finding critical numbers?

cruffo · Answer

1.) find the first derivative
2.) find numbers that make 1st derivative = 0 or undefined

did you find the 1st derivative?

cruffo · Answer

ok.. so 
$$f'(t) = 2\sin(t)\cos(t) + \sin(t)$$

anonymous · Answer

Sorry,internet disconnected.
Let me show you where I've gotten to.

anonymous · Answer

f prime of t = cos^2 t + sin t = 1 + sin t(1 - sin t)

cruffo · Answer

You need chain rule for that first term
$$\sin^2(t) = [\sin(t)]^2$$

anonymous · Answer

Oh my God!  Thanks a bunch cruffo!  I didn't properly differentiate sin^2(t), did I?  :P

cruffo · Answer

np : )

anonymous · Answer

$$\left\{\{t\to 0\},\left\{t\to -\frac{2 \pi }{3}\right\},\left\{t\to \frac{2 \pi }{3}\right\}\right\} $$

cruffo · Answer

$$\sin(t)(2\cos(t) + 1) = 0$$
sin(t) = 0 when t = any multiple of pi
2cos(t) + 1 = 0
2cos(t) = -1
cos(t) = -1/2
t = 2pi/3 + 2kpi or  4pi/3 +2kpi

cruffo · Answer

$$t = \left\{k\pi, \; \pm\frac{2\pi}{3} + 2k\pi\right\}$$