Suppose the Deflection D of a Beam of Length L $D = 6 x ^ { 4 } - 9 L x ^ { 3 } + 2 L ^ { 2 } x ^ { 2 }$

Multiple Choice

Suppose the deflection D of a beam of length L is $D = 6 x ^ { 4 } - 9 L x ^ { 3 } + 2 L ^ { 2 } x ^ { 2 }$ where $x$ is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

A) $x = 0.156 L$
B) $x = 0.363 L$
C) $x = 0.175 L$
D) $x = 0.362 L$
E) $x = 0.176 L$