What are the extrema of $f (x) = \frac{1}{x^{3}} + 10 x$ $f(x)=1/x^3 +10x$ on the interval [1,6]?

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Answer 1 · 2015-11-14T19:04:53

Always start with a sketch of the function over the interval.

On the interval [1,6], the graph looks like this:

enter image source here

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

hope that helped

What are the extrema of f(x)=1x3+10x f(x)=1/x^3 +10x on the interval [1,6]?