Question

Consider the function f(x) = e^sin(cos(x)) on the interval [0, 4π]

a) The critical points of f are at__________?
[Hint: The range of the function cos(x) is [−1, 1]. What is the range of the function cos(cos(x))?]

b) Local maxima are at ________?
Local minima are at ________?

c)Global maxima are at_______?
Global minima are at_______?

d) Consider the same function, but now defined for all real numbers. Does it have a global
maximum or minimum? Explain

Answer 1

Ok, we've done a bunch of these for you. What ideas do you have?

I'll get you started with

f'(x) = -sin(x) cos(cos(x)) e^sin(cos(x))

The rest is just algebra and trig.