Answer:
6 miles per hour
Step-by-step explanation:
Given the function [tex]g(x)=x^4-4x^2+7x-8[/tex]
It tells us the rate (speed) in miles per hour of the roller coaster at a time instant (x is the time).
If we want to find speed of roller coaster at 5 seconds, we will substitute 5 into x and find the value of g(x). that is the speed.
Similarly, in this problem we want the speed of the rollercoaster at time = 2 seconds, so we plug in 2 into x and find g(x), the speed. Shown below:
[tex]g(x)=x^4-4x^2+7x-8\\g(2)=(2)^4 -4(2)^2 +7(2) -8\\g(2)=16-16+14-8\\g(2)=6[/tex]
Hence, at 2 seconds, the roller coaster is going at 6 miles per hour
