We are given the curves

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

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

, passing through

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

, and

y=f(x)

, passing through

(0,1)

, where

f(x)>0

and

f(x)

is differentiable for all

x\in\mathbb{R}

. If tangents drawn to both curves at points with equal abscissae intersect at the same point on the

x

-axis, then the function

f(x)

is (1) increasing for all

x

(2) non-monotonic (3) decreasing for all

x

(4) None of these