he66666
  • he66666
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..
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Normal meas perpendicular. If the slope of one line is 0, then the slope of the normal must be undefined (vertical, in other words).
anonymous
  • anonymous
(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.)
he66666
  • he66666
I know it's vertical but how do you find the vertical slope? :S

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anonymous
  • anonymous
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?
anonymous
  • anonymous
Finally, since the vertical line passes through (1, 2), its equation must be x = 1.
he66666
  • he66666
Oh I get it. Thanks so much Bickford :)

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