A box is made from a rectangular sheet by cutting and folding so that its volume is V = 3x^3 - 15x^2 + 18x cm^3, where x cm is the height. Find the value of x at which V is stationary.

x = \dfrac{10 \pm 2\sqrt{7}}{6}

x = \dfrac{10 \pm 2\sqrt{7}}{3}

x = \dfrac{30 \pm 2\sqrt{7}}{6}

AM-2055

Stationary points

A Math · Secondary 4 · Hard · Stationary points

A box is made from a rectangular sheet by cutting and folding so that its volume is

V = 3x^3 - 15x^2 + 18x

^3

, where

x

cm is the height. Find the value of

x

at which

V

is stationary.

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