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#### DeusAbscondus

##### Active member

- Jun 30, 2012

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No matter how or what strategy I try, I can't get the optimum value for $x$ in the following equation:

$$V=4x^3-60x^2+200x$$ Let V=Volume of a rectangular prism, so:

$$V'=12x^2-60x+200$$ Set V'=0 to get turning point

$$12x^2-60x+200=0$$

The answer given in my text is when

$$ x=2.11 \Rightarrow \text{ the maximum volume is }\approx 192.45cm^2$$

I can graph it to get this, but can't get it using the quadratic formula for some reason.

some help would be appreciated

$$V=4x^3-60x^2+200x$$ Let V=Volume of a rectangular prism, so:

$$V'=12x^2-60x+200$$ Set V'=0 to get turning point

$$12x^2-60x+200=0$$

The answer given in my text is when

$$ x=2.11 \Rightarrow \text{ the maximum volume is }\approx 192.45cm^2$$

I can graph it to get this, but can't get it using the quadratic formula for some reason.

some help would be appreciated

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