Question

1. How can you tell that a point on the graph is a maximum or minimum?

2. How would you explain average rate of change to a classmate who was absent today? What does it tell us and how do we find it?

please give a simple summary of both answers after the explanations!!

Answer 1

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Answer:

1. there are no points higher than a maximum; no points lower than a minimum
2. average rate of change is the slope of a straight line connecting the points of interest.

Explanation:

1. A point on a graph is a maximum if there are no points on the graph that are higher.

A point on a graph is a minimum if there are no points on the graph that are lower.

Sometimes you're interested in a "local" maximum or minimum. In that case, the "no points higher/lower" rule refers to points in the immediate vicinity of the one of interest.

Sometimes you're interested in a maximum or minimum on an interval. In that case, the rule applies to points contained within the interval. (The maximum or minimum may be at the end of the interval.)

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2. Average rate of change is defined over some interval. That is, you are given the end points of the interval of interest. The average rate of change is the slope of a straight line between those end points. The slope formula applies:

`m=(y_2-y_1)/(x_2-x_1) \quad\text{where the end points of the interval are $(x_1,y_1)$ and $(x_2,y_2)$}`