I need to check my work. It is from a "fake" AP Calculus AB 2008 exam.
The line normal to 3x^2+4y+y^2=3
at x = m is parallel to the y-axis. What is m? the choices for the answers are
I used implicit differentiation to get a derivative of
dy/dx = (-6x)/(4+2y)
Won't the slope of the normal line be the neg. recip of this derivative function?
To be parallel to the y-axis, the slope is undefined so 6x = 0 and x = 0.
This means choice c is correct?
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Agreed. Looks correct.
I didn't do any of the math, but I read your method and it sounds just perfect.
Derive to get the slope, solve for dy/dx.
The line normal to this will be the negative reciprocal.
For it to be parallel to the y axis, it would have to be undefined. So yeah.
Or you could have just known that the line normal would be parallel when the tangent was 0 and solved it that way without taking the negative reciprocal. Both work.
Okay, and yeah. I went ahead and checked your implicit differentiation too. That checks out.