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zmudz

  • one year ago

Find the value of \(x\) that maximizes \(f(x) = \log (-20x + 12\sqrt{x}).\) If there is no maximum value, write "NONE".

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  1. misty1212
    • one year ago
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    HI!!

  2. misty1212
    • one year ago
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    looks like a calc problem right? take the derivative and find the critical points

  3. misty1212
    • one year ago
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    actually since the log is an increasing function, forget that part and maximize \[-20x+12\sqrt{x}\]

  4. anonymous
    • one year ago
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    maximize \(-20u^2+12u=-20(u^2-\frac35u)=-20(u-\frac3{10})^2+\frac95\) subject to \(u\ge0\)

  5. anonymous
    • one year ago
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    which obviously attains a maximum value of \(9/5\) (when \(x=3/10\)), so the maximum value of our expression is \(\log(9/5)=\log9-\log5\)

  6. anonymous
    • one year ago
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    ** when \(u=3/10\) rather

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