Question

Determine where f(x)= (x+ sin x) is increasing

Answer 1

take derivative and consider where it is positive

Answer 2

A function is increasing where its derivative is positive.

The derivative of f(x), f ' (x) = 1 + cos x

set 1 + cos x = 0

you get cos x = -1

This occurs at pi radians on [0, 2pi]

Now, you can finish the problem.

(I assumed the closed interval [0, 2pi])

Answer 3

well, the interval is actually negative infinity to positive infinity.
i think you have to solve for x and do the sign analysis.