anonymous
  • anonymous
Calculus question ; photo attached
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
abb0t
  • abb0t
Start by taking the derivative of your function. That will be your first step. Can you do that?
anonymous
  • anonymous
9+(2/x^2)=0?

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abb0t
  • abb0t
Great. Now that you have that, solve for "x".
stamp
  • stamp
@abb0t that derivative is incorrect.
abb0t
  • abb0t
Hmm, is it now? Well, @Dodo1 you need to try again then.
anonymous
  • anonymous
how is it wrong?
stamp
  • stamp
@abb0t Good luck evaluation that term = 0 without using imaginary numbers. @Dodo1 Forgot his - sign when taking the derivative using the power rule
anonymous
  • anonymous
9+(2x^(-2))=0?
stamp
  • stamp
no
stamp
  • stamp
\[9x+2x^{-1}\]\[9+(-1)2x^{-1-1}\]\[9-2x^{-2}\]\[9-2/x^2\]
stamp
  • stamp
@Dodo1 How did you plan on solving 9 + 2/x^2 = 0? It is not possible using real numbers because any real number squared is positive, this was the first clue that something was wrong with the derivative
anonymous
  • anonymous
oh not plus ok. I see
anonymous
  • anonymous
next step is mutiply x^2 both side?
anonymous
  • anonymous
@stamp
stamp
  • stamp
@Dodo1 It is algebra I at this point. Solve for x.
anonymous
  • anonymous
x=Sqrt(9/2) @stamp
stamp
  • stamp
\[9-2/x^2=0\]\[9=2/x^2\]\[x^2=2/9\]\[x=+/-(\sqrt2/3)\]
anonymous
  • anonymous
Ops sorry i did 9X^2+2=0
anonymous
  • anonymous
whats the next step? max at _sart(2)/3? @stamp
stamp
  • stamp
You do not need to tag me in every response, Dodo, I am here. These values, x = +/- c, are critical points. They are max or mins, we do not know until we consider each point with respect to the second derivative. You have been familiarized with the second derivative test in lecture, now we are using it to see which of these critical points are max, mins, etc.
stamp
  • stamp
I have to go, but this should help you enough to get started. Somebody else should be able to help you.
anonymous
  • anonymous
Yea, I do need to prepare derivative problems. Are you going?
stamp
  • stamp
f(x) = http://www.wolframalpha.com/input/?i=9x%2B2%2Fx f'(x) = http://www.wolframalpha.com/input/?i=derivative+of+9x%2B2%2Fx f''(x) = http://www.wolframalpha.com/input/?i=second+derivative+of+9x%2B2%2Fx critical points where f'(x) is 0 = http://www.wolframalpha.com/input/?i=solve+derivative+of+9x%2B2%2Fx graph of f(x) http://www.wolframalpha.com/input/?i=plot+9x%2B2%2Fx Visually one can observe that the negative critical point is a maximum, while the positive critical point is a minimum. Analytically, you can observe the change of f''(x) to the left of the critical point and to the right of the critical point. Since f'( - c ) goes from + to - , - c is a maximum. Since f'( + c ) goes from - to +, + c is a minimum.

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