x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3)?
(how do i solve using implicit differentiation?)

Question

x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3)? 
(how do i solve using implicit differentiation?)

misty1212 · Answer

HI!!

misty1212 · Answer

yes you do

misty1212 · Answer

twice

solomonzelman · Answer

you don't need implicit.

solomonzelman · Answer

$\large\color{#000000 }{ \displaystyle y=\sqrt{25-x^2}}$

misty1212 · Answer

no, but it will certainly make life easier!

solomonzelman · Answer

that is your f, because the point (4,3) is on the top half of the circle.

solomonzelman · Answer

$\large\color{#000000 }{ \displaystyle y=\sqrt{25-x^2}}$

differentiate twice, and plug in x=3

misty1212 · Answer

if you do it that way, first derivative is $$\frac{-x}{\sqrt{25-x^2}}$$ but then you have to find the derivative of that one!

solomonzelman · Answer

well, product rule (denominator written as neg exponent), wouldn't be so hard.

misty1212 · Answer

if you use implicit diff, first derivative is $$y'=-\frac{x}{y}$$ easier for me to deal with i think

anonymous · Answer

using implicit differentiation, how would you get the 2nd derivative?