Christiana wants to find the derivative of $f(x)=\cos\left(\dfrac{\pi}{2}x\right)$ at the point $x=2$. Her table below shows the average rate of change of $f$ over the intervals $[x,2]$ or $[2,x]$ for $x$-values that get increasingly closer to $2$: $x$|Interval|Average rate of change, $\dfrac{f(x)-f(2)}{x-2}$ :- | :- | :- $1.9$|$[1.9,2]$|$-0.1231$ $1.99$|$[1.99,2]$|$-0.0123$ $1.999$|$[1.999,2]$|$-0.0012$ $2.001$|$[2,2.001]$|$~~~0.0012$ $2.01$|$[2,2.01]$|$~~~0.0123$ $2.1$|$[2,2.1]$|$~~~0.1231$ **From the table, what does the derivative of $f(x)=\cos\left(\dfrac{\pi}{2}x\right)$ at $x=2$ appear to be?** [[☃ input-number 1]]