During this pandemic Mary and her friends decided to take a break from schoolwork and go on a hike up the Blue Mountain. When she was at the top of the mountain, she was able to view a valley, as seen below in Figure 1. She begun to visualise the shape when she realized that the mountain on the left forms a cubic function with the valley. Choose a suitable cubic function to answer the following questions: 1. Determine the maximum point of the mountain and the minimum point of the valley using the curve you have chosen. Hence calculate the height of the mountain if it measured by taking the height from the minimum point of the valley to the maximum point of the mountain. 2. Verify that the points found in part 1. is a minimum and maximum point. 3. Find the area under the mountain between two fix points of your choice that is feasible.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.