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AP Calc for Reiny

posted by on .

You did just fine and your second derivative is correct, if you meant (6y^2 - 4x^2)/(9y^3)
except they took it a bit further.

notice your numerator is
-4x^2 + 6y^2

from the original
2x^2 - 3y^2 = 4 , then
4x^2 - 6y^2 = 8 , and
-4x^2 + 6y^2 = -8

to get their -8/9y^3

If you were marked "wrong", then that is bad,
when differentiating implicitly, there are often multiple variations of the same answer.

Here is a way to check if two possible answers are equivalent:
Pick any point which satisfies the original equation, sub that point into the two variations of the derivatives, you should get the same answer if they are equivalent.
the point (√8,2) is on the original curve
y'' -- your answer -- = (24 - 32)/72 = -8/72 = -1/9
y'' -- their answer = -8/72 = -1/9

ok, then !!

When you wrote
2x^2 - 3y^2 = 4 , then
4x^2 - 6y^2 = 8 , and
-4x^2 + 6y^2 = -8
Did you just run a ratio for the first two equations? And, then for te third since it was negative, then you just took the negative number for it 8 to negative 8?
And, I was not marked wrong for it- it was a hw problem and the answer in the back had -8 but had gotten the -4x^2 + 6y^2 expression.
Also, how were you able to get the point (√8,2)as a point on the curve? Did you just solve for y? Thanks so much for your help.

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