Let ƒ : R → R be a twice differentiable function such that ƒ(x + y) = ƒ(x) ƒ(y) for all x, y ∈ R . If ƒ'(0) = 4a and ƒ satisfies ƒ''(x) – 3a ƒ'(x) – ƒ(x) = 0, a 0, then the area of the region R = {(x,y) | 0 ≤ y ≤ ƒ(ax), 0 ≤ x ≤ 2} is :

Question

Let ƒ : R → R be a twice differentiable function such that ƒ(x + y) = ƒ(x) ƒ(y) for all x, y ∈ R . If ƒ'(0) = 4a and ƒ satisfies ƒ''(x) – 3a ƒ'(x) – ƒ(x) = 0, a > 0, then the area of the region R = {(x,y) | 0 ≤ y ≤ ƒ(ax), 0 ≤ x ≤ 2} is :

Accepted Answer

e 2 – 1

Let ƒ : R → R be a twice differentiable function such that ƒ(x + y) = ƒ(x) ƒ(y) for all x, y ∈ R . If ƒ'(0) = 4a and ƒ satisfies ƒ''(x) – 3a ƒ'(x) – ƒ(x) = 0, a > 0, then the area of the region R = {(x,y) | 0 ≤ y ≤ ƒ(ax), 0 ≤ x ≤ 2} is :

Related JEE Main General questions