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## Homework Statement

'Use differentiation to prove that as the radius of the base of a cone increases, the height of the cone decreases.'

## Homework Equations

The height has been previously calculated as:

h = (507 - 2pi r^3) / pi r^2

## The Attempt at a Solution

I have worked out that:

h' = (-1014 - 2pi r^3) / pi r^3

I'm just not sure how to do the proving section though. I can do it without differentiating by replacing values for r in the h equation and also by graphing the h equation, but that doesn't answer the question as differentiation is not used. Any help would be greatly appreciated!