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Answer to Question #821 in Calculus for Max

Question #821
Where does the periodic function f(x) = 2e(sin x/2) 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) =( 2esin(x/2) )'= 2 sin (x/2) esin(x/2) * 1/2 cos (x/2) = 1/2 sin(x) esin(x/2) = 0;
As esin(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).

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