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

1 Answer
Nov 14, 2015


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


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

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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) #=1/216+60~~60.005#

hope that helped