how to find max( expression)?

Question

how to find max. for
$$\max(x^{2},x^{2a}),$$ where $x \geq 0$ and $0<a\leq 1$ (or $a \geq 1$).

i don't know if this correct in case $0<a\leq 1$ $$\max(x^{2},x^{2a})=x^{2}$$ and in case $a \geq 1$ $$\max(x^{2},x^{2a})=x^{2a}$$

Answer 1

HINT

Consider a part the trivial cases $x=0$ and $x=1$ and then the two cases

• $0< x < 1\implies x^2>x^n \qquad$ for $n>2$
• $x>1\implies x^2<x^n\qquad$ for $n>2$