Find the exact location of all the relative and absolute extrema of the function.

Question

h(x) = 3(x − 1)^2⁄3 with domain [0, 2]

Answer 1

The critical points are where the derivative of the function is zero or undefined.

In this case, the derivative is 2/(x-1)^(1/3) which is never 0 and is undefined at 1.

For the interval [0,2], both 0 and 2 are maxima (always try the endpoints and x=1 is a minimum. If you graph the function, it looks like a curvy v, with a cusp at one on the x axis. Had 0 and 2 not been included or if the range was all Real, there would be no maxima.