Question

Given the function defined by e^sinx for all x such that -pi < or equal to x and x is < or equal to 2pi.
Find the x- and y- coordinates of all the maximum and minimum points on that given interval. Justify your answer.

Answer 1

Find any critical points of the function in that interval and find the y-values for these critical points. Then find the y-values for the actual endpoints of the intervals and compare them to find the maximum and minimum points.

Answer 2

I tried that and I don't know if what I've done so far is correct:
f(x)=e^sinx
F'(x)=(cosx)e^sinx
(cosx)e^sinx=0
e^sinx=arccos(0)
sinx=ln(arccos(0))
x=arcsin(ln(arccos(0)))
x=0.4685

Answer 3

Your algebra is wrong.
Remember that of you apply arccos to both sides than it would also have to be applied to the e^sinx(so not really simplifying the equation).
A way that you could solve it would to separate both functions and solve separately for when cosx = 0 and for when e^sinx = 0.

Answer 4

^The derivative is correct though :)

Answer 5

Thank you!!

Answer 6

No problem :)

Answer 7

And remember to compare the y-value of those two points to the values of the endpoints of the interval since those can be maximum or minimum values as well.

Answer 8

Okay got it!