Question

Let f : [1, ∞) → [2, ∞) be a differentiable function such that f(1) = 2. If 6∫f(t) dt for t ∈ [0,x] = 3xf(x) – x³ – 5 for all x ≥ 1, the value of f(2) is ...

Answer 1

Given equation is

y/x = x + c

When x = 1, y = 2, then c = 1

Hence, the equation of the curve is

y/x = x + 1 

when x = 2, then y = 6

Thus, the value of f(2) is 6.