Question

which of the following is most likely to be a relative minimum for this graph?
a. (3, -4)
b. (-1, 0)
c. (4, 0)
d. (0.5, 8.1)

Explanation:

Step1: Understand the concept of relative minimum

A relative minimum is a point on the graph where the function changes from decreasing to increasing. It is a local low - point.

Step2: Analyze each option

• Option B \((-1,0)\) and Option C \((4,0)\) are x - intercepts (where \(y = 0\)). They are not relative minima as the function does not have a "valley" at these points.
• Option D \((0.5,8.1)\) is a relatively high - value point on the graph.
• Option A \((3,-4)\) is a point where the function changes from decreasing (to the left of \(x = 3\)) to increasing (to the right of \(x = 3\)). It is in a "valley" of the graph.

Answer:

A. \((3,-4)\)