Question

1. compare the number of relative extrema of the two functions. f(x) has __ relative extrema, and g(x) has __ relative extrema.

Explanation:

Step1: Recall definition of relative extrema

Relative extrema are local maxima and minima. A local maximum is a point where the function changes from increasing to decreasing, and a local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze \(f(x)\)

Looking at the graph of \(f(x)\), we can see that it has 1 local maximum and 1 local minimum. So in total, \(f(x)\) has 2 relative extrema.

Step3: Analyze \(g(x)\)

For the graph of \(g(x)\), it has 2 local maxima and 1 local minimum. So \(g(x)\) has 3 relative extrema.

Answer:

\(f(x)\) has 2 relative extrema, and \(g(x)\) has 3 relative extrema.