Let's say I have $f(x) = x + cos(x)$, a continous and differentiable function:
When I try to find a stationary point with 0 = f'(x), I get the first stationary point only: on (1.157, f(1.157)). How can I find all other stationary points? E.g: in a specific interval [10,22]?
Best Answer
Observe that
$$f'(x)=1-\sin x=0\iff \sin x=1\iff x=\frac\pi2+2n\pi\;,\;\;n\in\Bbb Z$$
Well, now check which ones of the above points lay on $\;[10,22]\;$ ...