## 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".

1. misty1212

HI!!

2. misty1212

looks like a calc problem right? take the derivative and find the critical points

3. misty1212

actually since the log is an increasing function, forget that part and maximize $-20x+12\sqrt{x}$

4. anonymous

maximize $$-20u^2+12u=-20(u^2-\frac35u)=-20(u-\frac3{10})^2+\frac95$$ subject to $$u\ge0$$

5. anonymous

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

6. anonymous

** when $$u=3/10$$ rather