Question

the graph of $y = x^{4}-2x^{2}+1$ is shown. which point is a relative maximum? a c d b

Explanation:

Step1: Recall the definition of relative maximum

A relative maximum is a point where the function changes from increasing to decreasing.

Step2: Analyze the graph

Looking at the graph of \(y = x^{4}-2x^{2}+1\), at point \(B\), the function has a "peak" in its local neighborhood. Before point \(B\) (as \(x\) approaches from the left), the function is increasing, and after point \(B\) (as \(x\) approaches from the right), the function is decreasing.

Answer:

B