Olivia wants to find the derivative of $g(x)=-5e^x$ at the point $x=0$.
Her table below shows the average rate of change of $g$ over the intervals $[x,0]$ or $[0,x]$ for $x$-values that get increasingly closer to $0$:
$x$|Interval|Average rate of change, $\dfrac{g(x)-g(0)}{x-0}$
:- | :- | :-
$-0.1$|$[-0.1,0]$|$-4.7581$
$-0.01$|$[-0.01,0]$|$-4.9751$
$-0.001$|$[-0.001,0]$|$-4.9975$
$0.001$|$[0,0.001]$|$-5.0025$
$0.01$|$[0,0.01]$|$-5.0251$
$0.1$|$[0,0.1]$|$-5.2585$
**From the table, what does the derivative of $g(x)=-5e^x$ at $x=0$ appear to be?**
[[☃ input-number 1]]