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Find the maximum value of \(2x + 2\sqrt{x(1-x)}\) when \(0 \leq x \leq 1.\)

 Jun 23, 2020
 #1
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I messed up, view Alan's answer below.

 Jun 23, 2020
edited by hugomimihu  Jun 23, 2020
 #2
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Hmm!

 

 Jun 23, 2020
 #3
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Ooh. Need to let Alan the Grapher do this one.

 

I'm not experienced enough!

 

I'll delete my answer now.

hugomimihu  Jun 23, 2020
 #4
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Differentiate the expression with respect to x.  Set the result to zero and find the value of x which makes it zero.  Plug this value back in to the first expression to find the maximum value of the expression.

Alan  Jun 23, 2020
 #5
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hi alan! thanks for answering. what do you mean by differentiate the expression though?

Guest Jun 23, 2020
 #6
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Differentiate the equation is calculus...

 

I haven't learned that but I'm learning it now with my Algebra brain...

 

https://www.mathsisfun.com/calculus/differential-equations.html

hugomimihu  Jun 23, 2020
 #7
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In calculus the slope of a curve is obtained by a process called differentiation.  If you haven't done any calculus then clearly you can't obtain the maximum this way!  What way have you been taught to obtain the maximum?

 Jun 23, 2020
 #8
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Ah, I'll assume you were talking to guest...

 

i haven't learned this yet so I thought using algebra was enough...

 

apparently not!

 

lesson learned, don't replace calculus with algebra.... thanks newton.

hugomimihu  Jun 23, 2020

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