Question

What is the equation of the normal to y= (x^2 + 3) / (x+1) at (1,2)?

the answer is x =1 but I don't get why.
I know that the slope is 0 (after substituting 1 into the derivative equation), so to find the normal of that slope, isn't it 0 also? I ended up with y=2, which is wrong..

Answer 1

Normal meas perpendicular. If the slope of one line is 0, then the slope of the normal must be undefined (vertical, in other words).

Answer 2

(The use of the word goes back to lenses. A "normal" ray of light hits the glass of the lens at right angles to the surface. A normal ray is not bent by the lens, at least on entry.)

Answer 3

I know it's vertical but how do you find the vertical slope? :S

Answer 4

Okay, you found the derivative and plugged in x=1 to get the slope, 0/2. Since "normal" means perpendicular, you want a slope that is perpendicular to 0/2. Two slopes are perpendicular if they are negative reciprocals of each other, like 3/5 and -5/3. In this case, the neg. recip. is -2/0. That's undefined, and vertical lines have an undefined slope. Does that help?

Answer 5

Finally, since the vertical line passes through (1, 2), its equation must be x = 1.

Answer 6

Oh I get it. Thanks so much Bickford :)