Answer
See graph
The slope of $f$ gets very steep when $x$ is increasing a lot
$g$ approximates the derivative of $f$ because 0.01 represents a small step for $x$
Work Step by Step
We are given the functions
$f(x)=3\sqrt x$
$g(x)=\frac{f(x+0.01)-f(x)}{0.01}$.
Determine $g(x)$ by plugging $f(x)$ into $g(x)$:
$g(x)=\frac{3\sqrt{x+0.01}-3\sqrt x}{0.01}$
We graph both functions.
We notice:
The slope of $f$ gets very steep when $x$ is increasing a lot
$g$ approximates the derivative of $f$ because 0.01 represents a small step for $x$
