Answer:
a) largest; 7; 6; 5
b) smallest; 2; 5
Explanation:
Without using calculus, you can still estimate the local maximum and minimum points of a function from a graph by looking for the highest and lowest points on the graph in a particular interval. Here are the steps to follow:
1. Determine the interval of interest. Look at the x-axis of the graph and identify the interval where you want to find the local maximum and minimum points.
2. Look for the highest and lowest points on the graph in the interval of interest. Identify the highest point on the graph and mark it as a local maximum. Similarly, identify the lowest point on the graph and mark it as a local minimum.
3. Check for any other potential local maximum or minimum points. Look for any other points on the graph that are higher or lower than the neighboring points. These could be potential local maximum or minimum points.
4. Verify your findings. Once you have identified potential local maximum and minimum points, check them by drawing tangents to the curve at those points. If the tangent is horizontal at the point, then it is a local maximum or minimum point. If the tangent is not horizontal, then it is not a local maximum or minimum point.
5. Note that this method only provides an estimate of the local maximum and minimum points, and it may not be accurate. Calculus provides a more precise method for finding local maximum and minimum points.