Chapter 4.2, Problem 86E

Roller coaster A portion of a roller coaster’s tracks can be modeled by the polynomial function $f\left(x\right)=0.0001\left(x^3-600x^2+90,000x\right),$ where $0\le x\le 400.f\left(x\right)$ represents the height of the roller coaster in feet and x represents the horizontal distance in feet.

a. Find the height of the roller coaster when $x=100$ yards.

b. Find the value(s) of x on the interval $\left[0,400\right]$ at which the height of the roller coaster is 0 yards.