A triangular prism has an equilateral triangle of side x cm as its cross-section and length (12 - x) cm. The total volume V cm^3 is given by V = \dfrac{\sqrt{3}}{4}x^2(12 - x). Find the value of x for which V is stationary.

AM-1916

Stationary points

A Math · Secondary 4 · Medium · Stationary points

A triangular prism has an equilateral triangle of side

x

cm as its cross-section and length

(12 - x)

cm. The total volume

V

^3

is given by

V = \dfrac{\sqrt{3}}{4}x^2(12 - x)

. Find the value of

x

for which

V

is stationary.

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