Let α, β ∈ ℜ be such that the function Testbook f(x) = {αx2 + 2βx - 3α , x < 2 (α + 2)x + (α - β) , x ≥ 2 is differentiable for all x ∈ ℜ. Find the value of 25(α + β).

Let f(x) = ax(x-1) for x 3. If f(x) is continuous for all x, not differentiable at x = 1, and f'(x) is continuous at x = 3, what is the value of q?

Let f(x) = ax(x-1) for x 3. If f(x) is continuous for all x, not differentiable at x = 1, and f'(x) is continuous at x = 3, what is the value of p?