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## Main Question or Discussion Point

Is there a way to do this without differentiation?

[itex]\left(a+b\right)^{p}[/itex] [itex]\leq a^{p}+b^{p}[/itex]

0<p<1 and a,b[itex]\geq[/itex] 0

pulling the a out of the the first part and dividing by it to get

[itex]\left(1+\frac{b}{a}\right)^{p}[/itex][itex]\leq 1+\frac{b}{a}^{p}[/itex]

This seems like the way to go but am stuck. Any suggestions? Thanks.

[itex]\left(a+b\right)^{p}[/itex] [itex]\leq a^{p}+b^{p}[/itex]

0<p<1 and a,b[itex]\geq[/itex] 0

pulling the a out of the the first part and dividing by it to get

[itex]\left(1+\frac{b}{a}\right)^{p}[/itex][itex]\leq 1+\frac{b}{a}^{p}[/itex]

This seems like the way to go but am stuck. Any suggestions? Thanks.