NEED ANSWERED ASAP Derivatives of exponential functions

Question

Determine the points on the interval [0, 2π] where f(x)= e^sinx+cosx 

Answer 1

cos(x) on the interval [0, 2π] goes from 1 to 1

sin(x) on the interval [0, 2π] goes from 0 to 0

So the function goes from e to e

cos(x) at [π/2, 3π/2] is 0 and 0
sin(x) at [π/2, 3π/2] is 1 and 1

So the function goes through e a total of 4 times

The max value would be e^Sqrt(2) and the min value e^-Sqrt(2)