amy0799
  • amy0799
consider the following function. f(x) = sqrt(9-x^2) Find the derivative from the left at x = 3. Find the derivative from the right at x = 3.
Mathematics
chestercat
  • chestercat
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thadyoung
  • thadyoung
find the derivaite, use chain rule, and then plug in 3 for every x
amy0799
  • amy0799
can you show me how?
ChillOut
  • ChillOut
Let \(u=sqrt(v)\) and \(v=9-x²\). What does the chain rule tells you?

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ChillOut
  • ChillOut
tell*
ChillOut
  • ChillOut
\(\frac{d}{dx}f(g(x))=f'(g(x))*g'(x))\)
Castiel
  • Castiel
Make it simpler yourself by writing \[(9-x ^{2})^{\frac{ 1 }{ 2 }}\] Now you could use that derivation rule \[\frac{ d }{ dx }x ^{n}= nx ^{n-1}\] after that you still have to multiply it with derivation of \[\frac{ d }{ dx}(9-x ^{2})\]
amy0799
  • amy0799
would it be 9-2x?
Castiel
  • Castiel
\[\frac{ d }{ dx }(9-x ^{2})\] =\[\frac{ d }{dx }9-\frac{ d }{dx }x ^{2}\] Now what is a derivative of a constant number like 9 here?
amy0799
  • amy0799
0
Castiel
  • Castiel
that means \[\frac{ d }{ dx }(9-x ^{2}) = -2x\]
amy0799
  • amy0799
so then how do i find the derivative from the left and right at x=3?
Jhannybean
  • Jhannybean
\[\lim_{x\rightarrow 3^{-}} (9-x^2)^{1/2}\]\[\lim_{x\rightarrow 3^+} (9-x^2)^{1/2}\]
amy0799
  • amy0799
do i just plug in 3 for both equation?
amy0799
  • amy0799
@ChillOut can you help me
triciaal
  • triciaal
|dw:1440964454314:dw|
amy0799
  • amy0799
how do i find the derivative from the left and right at x=3?
triciaal
  • triciaal
1 Attachment
triciaal
  • triciaal
from the left let x = -3 from the right let x = 3
amy0799
  • amy0799
i got the answer wrong
triciaal
  • triciaal
why
amy0799
  • amy0799
i dont know...
triciaal
  • triciaal
didn't you put 0?

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