Question

Consider the function f(θ)=cos^2θ+sinθ..find all the critical values in [-π/3, 2π/3]

Answer 1

\[f(x) = \cos^2 (x) + \sin(x)\]
\[f'(x) - 2 \cos(x) * \sin(x) + \cos(x) = \cos(x)(1-2\sin(x))\]
solve f'(x) = 0

Answer 2

so u set F'(x)=0? and plug in a value in the [ ]?

Answer 3

you have to solve f'(x) = 0
\[\cos(x)(1−2\sin(x)) = 0\]

Now you have to find the general solution to:
cos(x) = 0
and
1 - 2 sin(x) = 0
Then you use the solutions that's inside the interval [-π/3, 2π/3]

Answer 4

ty!