# What are the extrema of  f(x)=1/x^3 +10x on the interval [1,6]?

Nov 14, 2015

#### Explanation:

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) $= 11$
absolute maximum : f(6) $= \frac{1}{216} + 60 \approx 60.005$

hope that helped