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 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 m at x=2.5 km.