Calculus
# Extrema

If $f(x)=\frac{ax+b}{x^2+1}$ has a local maximum of $11$ at $x=1$, what is the value of $a+b$?

A cubic function $f(x)$ satisfies the following two conditions:

$A.$ $f(x)$ has an extreme value $-4$ at $x = 1\$ and

$B.$ $\displaystyle \lim_{x \to 0} \frac{f(x)}{x} = -4$.

What is the value of $f(4)$?