Answer
$3$
Work Step by Step
Apply Th.1: the derivative rule for inverses.
If $f(b)=a$, then
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=a}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=b}}$
We are given $f(2)=4,\qquad (a=4, b=2)$
and the slope at the point (2,4) ... (at x=2) is
$\displaystyle \left.\frac{df}{dx}\right|_{x=2}=\frac{1}{3}$
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=4}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=2}}=\frac{1}{\frac{1}{3}}=3$
