Compute d^2y/dx^2 at the point (3, 2). x^2-y^2 = 5

Question

Compute d^2y/dx^2 at the point (3, 2).     x^2-y^2 = 5

zehanz · Answer

You could try this:

First, write y as function of x:$$y^2=x^2-5 \Leftrightarrow$$$$y=\pm \sqrt{x^2-5}$$Now, there are two options for y, apparently. We can do away with the negative one, however, because the question is about the point (3, 2). So y is positive.

So we have:$$y=\sqrt{x^2-5}$$Now first calculate the derivative of y:$$\frac{ dy }{ dx }=\frac{ 1 }{ 2\sqrt{x^2-5} }\cdot 2x=\frac{ x }{ \sqrt{x^2-5} }$$If you differentiate again and set x=3, you're done...

anonymous · Answer

is the ans -5/8 ??

zehanz · Answer

It is! So did you get$$\frac{ d^2y }{ dx^2 }=-\frac{ 5 }{ (x^2-5)\sqrt{x^2-5} }$$This is rather tedious, because you have to use the Quotient Rule and then simplify...

Setting x=3 then gives =-5/8