Question

which point is the best approximation of the relative maximum of the polynomial function graphed below?
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a (-2.7,16)
b. (-1.8,15)
c. (-3.6,17)
d. (-7.2,19)

Explanation:

Step1: Understand the concept of relative maximum

A relative maximum of a function is a point where the function changes from increasing to decreasing. On a graph, it is a "peak" point.

Step2: Analyze the \(x\) - coordinate range

Looking at the graph, the \(x\) - value of the relative maximum is between \(- 3\) and \(- 2\).

Step3: Analyze the \(y\) - coordinate range

The \(y\) - value of the relative maximum is between \(15\) and \(17\).

Step4: Check the options

• Option A: \((-2.7,16)\) has \(x=-2.7\) (between \(-3\) and \(-2\)) and \(y = 16\) (between \(15\) and \(17\)).
• Option B: \(x=-1.8\) is not in the correct \(x\) - range (should be between \(-3\) and \(-2\)).
• Option C: \(x=-3.6\) is not in the correct \(x\) - range (should be between \(-3\) and \(-2\)).
• Option D: \(x=-7.2\) is not in the correct \(x\) - range (should be between \(-3\) and \(-2\)).

Answer:

A. \((-2.7,16)\)