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anonymous

  • 5 years ago

I have an exam tomorrow and need help with this problem to make sure I understand the material... Determine the y-coordinate of the critical point for f(x)=1/x+1/5-x

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  1. anonymous
    • 5 years ago
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    Did you take the derivative?

  2. anonymous
    • 5 years ago
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    yea i got \[f'(x)=-1/x^2+1/(5-x)^2\]

  3. anonymous
    • 5 years ago
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    Looks right. So where would this function be 0?

  4. anonymous
    • 5 years ago
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    ummm this is where i get stuck...could i try to get x's on one side

  5. anonymous
    • 5 years ago
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    Well, I think he means the function will have its critical point at f'(x) = 0. Just do 1/x^2 = 1/(5-x)^2, got it?

  6. anonymous
    • 5 years ago
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    then would you cross multiply...???

  7. anonymous
    • 5 years ago
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    See, if 1/x^2 = 1/(5-x)^2, then x^2 = (5-x)^2. (x^2)^1/2 = ((5-x)^2)^1/2 |x| = |5-x| x = 5/2 or -5 = 0... since -5 is not 0, x = 5/2.

  8. anonymous
    • 5 years ago
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    ok i see

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