Find the maximum and minimum values of the function.

Question

Find the maximum and minimum values of the function   on the interval $[0,\pi ]$

Maximum Value:

Minimum Value:

Answer 1

Hi Lola,

First find the critical points (critical points are when the derivative is zero or undefined). So let's find the derivative first.

g'(Θ) = 3-4cos(Θ)

g' is not undefined anywhere, so we only have to worry about when it is zero.

solve the equation g'(Θ) = 0

3-4cos(Θ) = 0

cos(Θ) = 3/4

Θ = cos^-1(3/4)

Now find the value of g at the critical points (the only critical point is Θ = cos^-1(3/4), and at the interval end points.

g(0) = ...?

g(π) = ...?

g(cos^-1(3/4)) = ...?

The largest of the above values will be your maximum, and the smallest will be your minimum.