Questions: How many critical points are there? How many are local maxima? How many are local minima? There is (are) □ critical point(s). Number of local minima: □ Number of local maxima: □

How many critical points are there? How many are local maxima? How many are local minima?

There is (are) □ critical point(s).

Number of local minima: □

Number of local maxima: □

Transcript text: How many critical points are there? How many are local maxima? How many are local minima? There is (are) $\square$ critical point(s). Number of local minima: $\square$ Number of local maxima: $\square$

Solution

Solution Steps

Step 1: Identifying Critical Points

Critical points occur where the derivative of the function is zero or undefined. In this graph, the function is smooth, so we look for where the tangent line would be horizontal (i.e., slope of zero). There are no such points on this graph.

Step 2: Identifying Local Minima

Local minima are points where the function reaches a low point in a small neighborhood around that point. On the given graph, there are no such low points.

Step 3: Identifying Local Maxima

Local maxima are points where the function reaches a high point in a small neighborhood around that point. The graph also does not display any such high points.