Question

How do you find the critical numbers of `f(x) = x + 2sinx`?

Answer 1

The critical points are `x = (4pi)/3 + 2pin and (2pi)/3 + 2pin`

Explanation:

The derivative of the function is

`f'(x) = 1 + 2cosx`

Critical points will occur whenever the derivative equals `0` or is undefined.

`0 = 1 + 2cosx`

`-1 = 2cosx`

`-1/2 = cosx`

`x = (4pi)/3 + 2pin and (2pi)/3 + 2pin`

Hopefully this helps!