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he66666

  • 5 years ago

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..

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

  2. anonymous
    • 5 years ago
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    (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.)

  3. he66666
    • 5 years ago
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    I know it's vertical but how do you find the vertical slope? :S

  4. anonymous
    • 5 years ago
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    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?

  5. anonymous
    • 5 years ago
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    Finally, since the vertical line passes through (1, 2), its equation must be x = 1.

  6. he66666
    • 5 years ago
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    Oh I get it. Thanks so much Bickford :)

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