Question #821

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.

Expert's answer

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).

f'(x) = 0.

f'(x) =( 2e

As e

sin (x) = 0;

x = Pi n , n = Z (integers).

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