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Shidah · Jun 16, 2008, 12:28 AM

how to differentiate A=4x^2 + 216/x? I got stuck at 216/x?

Capuchin · Jun 16, 2008, 12:40 AM

$\frac{1}{x} = x^{-1}$

therefore:

$4x^2 + \frac{216}{x} = 4x^2 + 216x^{-1}$

Go from there

Shidah · Jun 16, 2008, 01:06 AM

Originally Posted by Capuchin

$\frac{1}{x} = x^{-1}$

therefore:

$4x^2 + \frac{216}{x} = 4x^2 + 216x^{-1}$

Go from there

so, it will be 8x - 216x^-2?

the full question is given a rectangular ( 2x by x by x)
the volume is 72cm3.
the total surface area is A=4x^2 + 216/x.
find the minimum value of the total surface area?

i don't know how to start.

Capuchin · Jun 16, 2008, 03:30 AM

Originally Posted by Shidah

so, it will be 8x - 216x^-2?

the full question is given a rectangular ( 2x by x by x)
the volume is 72cm3.
the total surface area is A=4x^2 + 216/x.
find the minimum value of the total surface area?

i dont know how to start.

That's right, so now you know that when dA/dx is 0, A is either at a maximum, minimum, or a reflex point. To find out which, you can look at d^2A/dx^2 , which should be positive for a minimum.

Unknown008 · Jun 17, 2008, 05:16 AM

And solve for dA/dx = 0