zmudz
  • zmudz
Find the value of \(x\) that maximizes \(f(x) = \log (-20x + 12\sqrt{x}).\) If there is no maximum value, write "NONE".
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
looks like a calc problem right? take the derivative and find the critical points
misty1212
  • misty1212
actually since the log is an increasing function, forget that part and maximize \[-20x+12\sqrt{x}\]

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anonymous
  • anonymous
maximize \(-20u^2+12u=-20(u^2-\frac35u)=-20(u-\frac3{10})^2+\frac95\) subject to \(u\ge0\)
anonymous
  • anonymous
which obviously attains a maximum value of \(9/5\) (when \(x=3/10\)), so the maximum value of our expression is \(\log(9/5)=\log9-\log5\)
anonymous
  • anonymous
** when \(u=3/10\) rather

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