17. Define by f(x) = 1/(1 + x2). Prove that f has a maximum and find the point at which that maximum occurs.
Thanks
Since $\displaystyle \forall x \in \mathbb{R}, x^2 \geq 0 \text{ Equality at x=0}$
$\displaystyle \Rightarrow 1+x^2 \geq 1 \text{ Equality at x=0}$
$\displaystyle \Rightarrow \frac1{1+x^2} \leq 1 \text{ Equality at x=0}$
Thus f(x) is bounded above by 1(its also the lub and hence the maxima).
We also see that maxima occurs at 0.