Question

the path of a roller coaster after it has reached the top of the first hill follows a polynomial function, as shown in the graph. use the graph to answer questions 7 - 10.

1. target g

at which value of x is there a relative maximum for f(x) on the interval 200 ≤ x ≤ 500?
a. 350
b. 300
c. 200
d. 250
e. 400

Explanation:

Step1: Understand Relative Maximum

A relative maximum on a graph is a point where the function changes from increasing to decreasing (the peak of a "hill" on the graph). We need to find this point in the interval \(200 \leq x \leq 500\).

Step2: Analyze the Graph

Looking at the graph of the roller coaster path:

• The x - axis represents distance (in feet) from \(0\) to \(500\), and the y - axis represents height (in feet).
• In the interval \(200 \leq x \leq 500\), we observe the shape of the graph. The graph has a peak (relative maximum) around \(x = 250\) (by visually inspecting the graph, we can see that between \(x = 200\) and \(x = 500\), the highest point (where the graph changes from increasing to decreasing) occurs at \(x = 250\)).

Answer:

D. 250