Problem

Let

f(x)

be differentiable function on the interval

(-\infty, \infty)

such that

f(1) = 5

and

\lim_{a \to x} \frac{af(x) - xf(a)}{a - x} = 2

, for all

x \in \mathbb{R}

. Then, which of the following alternative(s) is/are correct? a.

f(x)

has an inflection point b.

f'(x) = 3, \forall x \in \mathbb{R}

\int_{0}^{2} f(x) dx = 10

d. Area bounded by

f(x)

with coordinate axes is

(2/3)