What are the extrema of # f(x)=1/x^3 +10x# on the interval [1,6]?
Always start with a sketch of the function over the interval.
On the interval [1,6], the graph looks like this:
As observed from the graph, the function is increasing from 1 to 6. So, there is no local minimum or maximum .
However, the absolute extrema will exist at the endpoints of the interval:
absolute minimum : f(1)
absolute maximum : f(6)
hope that helped