How does one raise one's self?
Calculus
Level
1
\[\begin{eqnarray} 1^1 &=& 1 \\ 2^2 &=& 4 \\ 3^3 &=& 27 \\ 4^4 &=& 256 \\ 5^5 &=& 3125 \end{eqnarray} \]
Victoria just started learning about exponentiation in class, and she has written down the 5 equations above. She then postulates that
\(x^x\) is a strictly increasing function for positive \(x\).
Is her claim correct?
by
Pi Han Goh