If 3x^2 + y^2 = 7 then evaluate the second derivative of y with respect to x when x = 1 and y = 2. Round your answer to 2 decimal places.

Question

tmagloire1 · Answer

@jim_thompson5910

coconutjj · Answer

In order to evaluate the second derivative, you must first know the first derivative. Do you know how to differentiate implicitly

tmagloire1 · Answer

Yes the first derivative is -3x/y

coconutjj · Answer

dy/dx = -3x/y right? Now what is d/dx(-3x/y)

coconutjj · Answer

$$\frac{ -3y-(-3x)\frac{ dy }{ dx } }{ y^2 }$$

tmagloire1 · Answer

oh  i tustve messed up somewhere but ok i understand that part

coconutjj · Answer

now what does dy/dx equal to ?

tmagloire1 · Answer

what do you mean? when i plug in 1 and 2?

coconutjj · Answer

We just solved for dy/dx, dy/dx = -3x/y remember ?

tmagloire1 · Answer

yeah

coconutjj · Answer

so plug it in and simplify

tmagloire1 · Answer

plug it into the first or second derivative?

coconutjj · Answer

well, which one seems more logical?
1. Plugging in to 1st derivative solving for second derivative
2. Plugging into 2nd derivative solving for second derivative

tmagloire1 · Answer

I see the 1st

tmagloire1 · Answer

-3(1)/(2) = -3/2

coconutjj · Answer

No... not quite.. I don't know how you would approach the 1st. 2nd one is correct

tmagloire1 · Answer

-3(2)+3(1)/2^2 = -6+3/4 = -3/4

coconutjj · Answer

Remember it is $$\frac{ d^2y }{dx^2 }$$ = ...

coconutjj · Answer

$$\frac{ -3y - (3x)(\frac{ -3x }{ y }) }{ y^2 }$$

tmagloire1 · Answer

-3(2)+3(1)(-3/2)/2^2 = -21/8

coconutjj · Answer

you should be correct if you did the calculations correct.

tmagloire1 · Answer

ok thank you for your help!