The tangent line will be of the form .
We can get the slope from the derivative:
At x = 2 this becomes:
So we need the intercept. At x = 2 we know that y = 1, so
So the tangent line is
The line normal to this will have a slope of , so the form of the normal line will be and passes through (2, 1), so
So the normal line is .
(Sorry about the graph. The lines don't look perpendicular because the x and y scales are different. I haven't figured out how to fix this yet.)
-Dan