`f(x) = (x - 3)^(1/3)` Find the critical numbers, open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.
You need to evaluate the critical values, hence, in order to do so, you must solve for x the equation `f'(x) = 0` .
You need to find `f'(x), ` such that:
`f'(x) = (1/3)(x-3)^(1/3-1) => f'(x) = 1/(3*(root(3)(x-3)^2))`
You need to evaluate `f'(x) = 0` :
`1/(3*(root(3)(x-3)^2)) = 0`
There is no value of x to verify the equation `f'(x) = 0` , hence, there are no critical points.
Notice that the derivative is positive on R, hence, the function is increasing on R.