GATE Mechanical Engineering (ME) 2016 Shift 2 Solved Paper

A simply supported beam of length 2L is subjected to a moment M at the mid-point x = 0 as shown in the figure. The deflection in the domain 0 ≤ x ≤ L is given by
$\mathit{w}=\frac{-\mathit{M}\mathit{x}}{12\mathit{E}\mathit{I}\mathit{L}}\left(\mathit{L}-\mathit{x}\right)\left(\mathit{x}+\mathit{c}\right)$
Where E is Young’s modulus, I is the area moment of inertia and c is a constant (to be determined).

The slope at the centre x = 0 is