Question

x = 2 is which of the following extrema? *
10 points
relative maxima
relative minima
absolute maxima
absolute minima

Explanation:

Step1: Understand the definitions

• Relative minima: A point where the function changes from decreasing to increasing.
• Relative maxima: A point where the function changes from increasing to decreasing.
• Absolute minima: The lowest point of the entire function.
• Absolute maxima: The highest point of the entire function.

Step2: Analyze the graph at \(x = 2\)

Looking at the graph of \(y = f(x)\) at \(x=2\), the function changes from decreasing (to the left of \(x = 2\)) to increasing (to the right of \(x = 2\)). Also, it is not the lowest point of the entire function (since the function goes to \(-\infty\) as \(x\to - 2^{-}\)) and not the highest point (since there is a higher point to the left of \(x = 2\)).

Answer:

relative minima