Problem

We are given the curves

y = \int_{-\infty}^{x} f(t)\,dt

through the point

\left(0, \frac{1}{2}\right)

and

y = f(x)

, where

f(x) > 0

and

f(x)

is differentiable,

\forall x \in \mathbb{R}

through

(0, 1)

. If tangents drawn to both the curves at the points with equal abscissae intersect at the same point on the X-axis, then The function

f(x)

is a. increasing for all

x

b. non-monotonic c. decreasing for all

x

d. None of these