Function problem (e^sin(x))

Given the function defined by y=e^(sin(x)) for all x such that -(pie)<x<2(pie)
a) find the x and y coordinates of all maximum and minimum points on the given interval. Justify your answers
c) write an equation for the axis of symmetry of the graph

This is an AP exam question that is worth nine points (i cut out question b b/c it asks for sketching graph).

Currently i have took the derivative of e^sin(x) and found cos(x)*e^sin(x). Setting the derivative equal to 0 i found +pie/2, 3pie/2. After that i drew a line graph of when the graph increases and decreases when connecting these critical points. I recieved + for all sections. But heres the problem, i double checked by graphing on the calculator and it showed me a graph with alternating increases and decreases. Why is that? i've been stuck on this for an hour and i still can't seem to solve it. and i don't know what part b is asking. can someone help me please, im tired and restless but this homework is extremely important. guess it was absolutely fault for doing it so late anyways -_-" argh. thanks

also when i graphed by hand, i also got a different image. and i double checked my plug-in equation for my calculator and it was fine. this is frustrating and weird.
 
okay i found my mistake in question a. but i believe the answer is pie/2 because that is the point where the graph is divided in two. correct me if im wrong. but im glad i have answers. finally could sleep lols
 

J$C

15
0
You have the right derivative, and the right critical values. To tell whether the function is at a max or a min at these points, look to see if the derivative is going from positive to negative (max) or negative to positive (min) at your critical points. Conveniently enough cos(x)*e^sin(x) follows the same +/- trend as just cos(x). This is because e^sin(x) is always positive.

I attached graphs of the function and its derivative so you can see this.

Also, pie=delicious whereas pi=3.14159...
 

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