A derivative problem

Calculus Level 5

Let \[ f_k(x) =0 ; when \quad x < k\]and \[f_k(x)=1 ; when \quad x \ge k\]. The function 'T' is defined to be \[T_k(x) = \dfrac{d}{dx} (f_k(x))\] Suppose\[\dfrac{d^2 g(x)}{dx^2} = T_1(x) + T_2 (x)\] and \[g(0) = g'(0) = 0\] Find \(\displaystyle{g(5)}\)

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