Question 12
We indicate by $m(a, b)$ the arithmetic mean of the positive real numbers $a$ and $b$. Given the positive real function $g$ that has the first and the second positive derivatives, we define the mean $\mu(a, b)$ relative to the function $g$ by means of $$
2 g(\mu(a, b))=g(a)+g(b)
$$ say, Reasonedly, which of the two means $m$ and $\mu$ is greater.
2 g(\mu(a, b))=g(a)+g(b)
$$ say, Reasonedly, which of the two means $m$ and $\mu$ is greater.