### Home > PC3 > Chapter Ch8 > Lesson 8.1.2 > Problem8-28

8-28.

The tiny town of Twinpolypeaks is located next to a lake, both of which are in between two mountain peaks. The profile of the landscape can be modeled by the function $f(x)=-0.0005(x+3)(x+1)(x-1)^5(x-4.5)$ where $x$ is horizontal distance in miles and $f(x)$ is miles above sea level. The lake is below sea level and the town is above sea level.

1. Sketch the graph of the profile of the landscape. Use an appropriate domain.

The function has roots of $x=−3$, $−1$, $1$, and $4.5$.
The leading coefficient is negative.

2. If the width of the lake is captured in the profile of the landscape, approximately how wide is the lake?

Where is the curve significantly below the $x$-axis?

3. Approximately how wide is the town if there is nothing above $100$ feet over sea level?

What portion of the curve seems to be between the two 'mountains'?