Using the Mean Value Thoerem for this Inequality?

[JoshMaths]

Homework Statement

Let p > 1 and x > y > 0 Use the MVT to prove the inequality

py^(p-1)[x-y] =< x^p - y^p =< px^(p-1)[x-y]

The Attempt at a Solution

The only way i only how to use the MVT is where i already have the function. Do you have to define the function from the problem? Thanks for your help.

J

 

[LCKurtz]

Homework Statement

Let p > 1 and x > y > 0 Use the MVT to prove the inequality

py^(p-1)[x-y] =< x^p - y^p =< px^(p-1)[x-y]

The Attempt at a Solution

The only way i only how to use the MVT is where i already have the function. Do you have to define the function from the problem? Thanks for your help.

J

Yes, that's exactly what you have to do. Remember the MVT says$$
f(b)-f(a) = f'(c)(b-a)$$ where $c$ is between $a$ and $b$. Look carefully at your problem and see if you can't figure out an f(x) that might work. You need f(x) and its derivative in there. And you have x and y instead of a and b. Worry about the inequality signs after you come up with a likely f(x).