Question

Tory plans to enter the path at mile marker 1 and hike for 4 miles. Tory is a beginner hiker, so he wants to choose the path that is less steep on average.

Which path should he choose? Why?

Answer 1

If you need help visualizing this, you might draw vertical lines at distance = 1 and at distance = 5. Look at the points where those lines cross f(x). The vertical difference is perhaps 350 ft. Look at where the lines cross g(x). That vertical distance may be about 200 ft.

The vertical change from 1 to 5 is considerably less for g(x) than for f(x).

Tory should choose path ...
g(x)