Q2. Does f(x) achieve a relative maximum when x = -4?

Background

Topic: Relative Extrema (Maximum/Minimum) from a Graph

This question tests your ability to identify relative maxima and minima by analyzing the graph of a function.

Key Terms:

• Relative Maximum: A point where the function value is higher than at nearby points.

• Relative Minimum: A point where the function value is lower than at nearby points.

Step-by-Step Guidance

1. Examine the graph at to see if the function value is higher than at points immediately to the left and right.

2. Check the slope of the curve near . If the curve changes from increasing to decreasing, this indicates a relative maximum.

3. Compare the function value at with nearby values to confirm if it is indeed a peak.

4. Consider whether the endpoint or open circle at affects the classification as a relative maximum.

Try solving on your own before revealing the answer!