Figure 1.
Exercise #51 in Section 3.1 of Stewart asks the reader to find a normal to the graph of f(x) = 1 - x2 at the point (2, -3).
Taking the first derivative, f'(x) = -2x, hence the slope of the tangent line to the graph of f at the point (2, -3) is f'(2) = -2(2) = -4. Hence, the slope of the normal line will be the negative reciprocal; i.e., 1/4.
The reader can now use the point slope formula to determine the equation of the normal line,
or equivalently,
One can now enter the equation of f and the equation of the normal line as shown in Figure 1.
Figure 1.
However, if the user has scaled the axes in previous plots, one unit of length on the x-axis might not equal one unit of length on the y-axis, which distorts the image. As a result, the line normal to the graph of f at A does not look perpendicular to the graph of f (see Figure 1).
However, there is an easy fix. Ctrl-Click the window with your mouse, then select xAxis : yAxis from the popup menu, then select 1:1. This will make one unit of length on the x-axis equal in length to one unit of length on the y-axis. As a result, the normal line now looks perpendicular to the graph of f at the point (2, -3) (see Figure 2).
Figure 2.
I hope this helps.