Question

question 9 of 10
which of the following is most likely to be a relative minimum for this graph?
a. (3, -4)
b. (4, 0)
c. (-1, 0)
d. (0.5, 8.1)

Explanation:

Step1: Recall the definition of relative minimum

A relative minimum is a point on the graph where the function changes from decreasing to increasing. It is a "valley" point.

Step2: Analyze each option

• Option B \((4,0)\) and Option C \((-1,0)\) are x - intercepts (where \(y = 0\)). They are not "valley" points.
• Option D \((0.5,8.1)\) is a "peak" (a relative maximum) since the function changes from increasing to decreasing at that point (assuming the general shape of the graph).
• Option A \((3,-4)\) is in the "valley" of the graph. At this point, the function changes from decreasing (to the left of \(x = 3\)) to increasing (to the right of \(x=3\)).

Answer:

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