Answer to Question #821 in Calculus for Max

Question

Where does the periodic function f(x) = 2e[sup](sin x/2)[/sup] take on its extreme values andwhat are these values?&
Show all working and explain your answer clearly.

Answer 1

To find extreme points we have to solve the equation:
f'(x) = 0.

f'(x) =( 2e^sin(x/2) )'= 2 sin (x/2) e^sin(x/2) * 1/2 cos (x/2) = 1/2 sin(x) e^sin(x/2) = 0;
As e^sin(x/2) is always greater than 0, we can solve the equation only for sin(x) :


sin (x) = 0;
x = Pi n , n = Z (integers).