12.4 Exercise 66

Numerically evaluate the derivative. Explore the behavior of the graph of $f \left(x\right) = x^{2}$ around $x = 1$ by graphing the function on the following domains: $\left[0.9 , 1.1\right]$, $\left[0.99 , 1.01\right]$, $\left[0.999 , 1.001\right] ,$ and $\left[0.9999 , 1.0001\right]$ . We can use the feature on our calculator that automatically sets Ymin and Ymax to the Xmin and Xmax values we preset. (On some of the commonly used graphing calculators, this feature may be called ZOOM FIT or ZOOM AUTO). By examining the corresponding range values for this viewing window, approximate how the curve changes at $x = 1 ,$ that is, approximate the derivative at $x = 1.$