Questions: Refer to the graph at the right to answer the following questions. (a) At which labeled points is the function increasing? (b) At which labeled points is the graph concave up? (c) Which labeled point has the most positive slope?

Refer to the graph at the right to answer the following questions.
(a) At which labeled points is the function increasing?
(b) At which labeled points is the graph concave up?
(c) Which labeled point has the most positive slope?

Transcript text: Refer to the graph at the right to answer the following questions. (a) At which labeled points is the function increasing? (b) At which labeled points is the graph concave up? (c) Which labeled point has the most positive slope?

Solution

Solution Steps

Step 1: Identify where the function is increasing

The function is increasing where the slope of the graph is positive. From the graph, the function is increasing between points B and D.

Step 2: Identify where the graph is concave up

The graph is concave up where the second derivative is positive, which typically looks like a "U" shape. From the graph, the function is concave up between points C and E.

Step 3: Identify the point with the most positive slope

The point with the most positive slope is where the graph is steepest in the upward direction. From the graph, this occurs at point C.