A continuous function models the height (in meters relative to sea level) of a hiker…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A continuous function

h

models the height (in meters relative to sea level) of a hiker along a trail, where

x

is the horizontal distance in kilometers from the trailhead. If

h(0)=150

and

h(5)=-20

, which statement must be true? (a) The hiker crossed sea level exactly once for some

x

\, in

(0,5)

. (b) The hiker's instantaneous rate of change in height equaled

-34\text{ m/km}

at some point in

(0,5)

. (c) The hiker crossed sea level at least once for some

x

\, in

(0,5)

. (d) The hiker reached an altitude of exactly

75\text{ m}

x=2.5\text{ km}