What are the absolute extrema of #f(x)=9x^(1/3)-3x in[0,5]#?
The absolute maximum of
To find the absolute extrema of a function, we need to find its critical points. These are the points of a function where its derivative is either zero or does not exist.
The derivative of the function is
We also have to consider the endpoints of the function when looking for absolute extrema: so the three possibilities for extrema are