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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".
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".

This Question is Closed

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2looks like a calc problem right? take the derivative and find the critical points

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2actually since the log is an increasing function, forget that part and maximize \[20x+12\sqrt{x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0maximize \(20u^2+12u=20(u^2\frac35u)=20(u\frac3{10})^2+\frac95\) subject to \(u\ge0\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which 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
 one year ago
Best ResponseYou've already chosen the best response.0** when \(u=3/10\) rather
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