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## Homework Statement

Let y be a fixed real number satisfying 0<y[tex]\leq[/tex]1. Prove that (1+x)[tex]^{y}[/tex][tex]\leq[/tex]1+ x[tex]^{y}[/tex] for all x[tex]\geq[/tex]0.

## Homework Equations

I'm not sure.

## The Attempt at a Solution

The hint given with the problem states that the derivative of x[tex]^{y}[/tex] is yx[tex]^{y-1}[/tex]. My first thought is that I'm supposed to show that they are both strictly increasing, but I don't really know what that would help me with.

I'm not really looking for an answer so much as a bit of direction.