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

Background

Topic: Relative Extrema & Graph Analysis

This question tests your ability to identify relative maxima from a graph. A relative maximum occurs at a point where the function changes from increasing to decreasing.

Key Terms:

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

• Critical Point: Where the derivative is zero or undefined.

Step-by-Step Guidance

1. Examine the graph at . Look for a peak or turning point at this location.

2. Check if the function increases before and decreases after . This would indicate a relative maximum.

3. Observe the behavior of the curve near to see if it matches the definition of a relative maximum.

Try solving on your own before revealing the answer!