A box has length x cm, width (5-2x) cm and height (3-x) cm. Show that its volume V cm^3 is V = 2x^3 -11x^2 +15x. Then, find the value of x for which V is stationary.

x = \frac{5}{3} or x = \frac{3}{2}

x = \frac{5}{2} or x = \frac{3}{2}

x = \frac{11+\sqrt{31}}{6} or x = \frac{11-\sqrt{31}}{6}

AM-2054

Stationary points

A Math · Secondary 4 · Hard · Stationary points

A box has length

x

cm, width

(5-2x)

cm and height

(3-x)

cm. Show that its volume

V

^3

V = 2x^3 -11x^2 +15x

. Then, find the value of

x

for which

V

is stationary.

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