Question

Identify the critical points and find the extreme values on the interval [-1,-5) for f(x)=cosx+xsinx+3

I've taken the derivative which gives me f'(x)=xcos(x). I know I have to solve to get the critical points and then plug in the critical points that are on the interval and the interval points to get the extreme values. I'm just not sure how to do those parts with this particular function. Please help

Answer 1

The critical points are where f' is zero or undefined. It is never undefined. So, remembering your Algebra I,

f' = 0 when x=0
or cosx=0: x = odd multiples of ?/2

x=0 is not in the domain, so the only critical points are at x = -?/2 and -3?/2.

Naturally, the extreme values also occur there.

http://www.wolframalpha.com/input/?i=cosx%2Bxsinx%2B3+for+-5+%3C+x+%3C%3D+-1