- #1
bobcat817
- 9
- 0
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.