Question

1. rollercoaster the height of a rollercoaster compared to the distance from start is shown in the graph. determine whether points b, c, d, and f are relative minima, relative maxima, or neither. describe what each value means in the context of this situation.

Explanation:

Step1: Recall definitions

A relative maximum is a point where the function changes from increasing to decreasing. A relative minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze point B

At point B, the roller - coaster height changes from increasing to decreasing as the distance from the start increases. So, B is a relative maximum. It means the roller - coaster reaches a local high point at this distance from the start.

Step3: Analyze point C

At point C, the roller - coaster height changes from decreasing to increasing as the distance from the start increases. So, C is a relative minimum. It means the roller - coaster reaches a local low point at this distance from the start.

Step4: Analyze point D

At point D, the roller - coaster height changes from increasing to decreasing as the distance from the start increases. So, D is a relative maximum. It means the roller - coaster reaches a local high point at this distance from the start.

Step5: Analyze point F

At point F, the roller - coaster height changes from decreasing to increasing as the distance from the start increases. So, F is a relative minimum. It means the roller - coaster reaches a local low point at this distance from the start.

Answer:

• Point B: Relative maximum. The roller - coaster reaches a local high point at this distance from the start.
• Point C: Relative minimum. The roller - coaster reaches a local low point at this distance from the start.
• Point D: Relative maximum. The roller - coaster reaches a local high point at this distance from the start.
• Point F: Relative minimum. The roller - coaster reaches a local low point at this distance from the start.