- #1

Arnoldjavs3

- 191

- 3

## Homework Statement

Suppose that x,y are in (0,0.5). Show that:

$$\left|\frac{1}{x^3}-\frac{1}{y^3}\right| ≥ 48|x-y|$$

## Homework Equations

## The Attempt at a Solution

I think that we need a function ##f(t) = t^{-3}## & ##f'(t) = -3t^{-4}##. Now we use the MVT here to show that there is some c that makes the expression in the problem correct right? My question is how do I incorporate the absolute value notations in the statement here?

$$-3c^{-4} = \frac{f(y) - f(x)}{y-x}$$

I think we have to assume that either x or y is greater than the other(because if they were equal then the above owuld be proven). Do I just input c for 0.5? I'm unsure.