anonymous
  • anonymous
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?)
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
yes you do
misty1212
  • misty1212
twice

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SolomonZelman
  • SolomonZelman
you don't need implicit.
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle y=\sqrt{25-x^2}}\)
misty1212
  • misty1212
no, but it will certainly make life easier!
SolomonZelman
  • SolomonZelman
that is your f, because the point (4,3) is on the top half of the circle.
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle y=\sqrt{25-x^2}}\) differentiate twice, and plug in x=3
misty1212
  • misty1212
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
  • SolomonZelman
well, product rule (denominator written as neg exponent), wouldn't be so hard.
misty1212
  • misty1212
if you use implicit diff, first derivative is \[y'=-\frac{x}{y}\] easier for me to deal with i think
anonymous
  • anonymous
using implicit differentiation, how would you get the 2nd derivative?

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