Question

based on the graph of f(x) below, which of the following statements is true about f(x)?
a. f(x) has a relative minimum at x = -1.2 and a relative maximum at x = 1.2.
b. f(x) has a relative minimum at x = 2.2 and a relative maximum at x = -0.2.
c. f(x) has a relative maximum at x = -1.2 and a relative minimum at x = 1.2.
d. f(x) has a relative maximum at x = 2.2 and a relative minimum at x = -0.2.

Explanation:

Step1: Recall relative - extrema definition

A relative maximum occurs where the function changes from increasing to decreasing, and a relative minimum occurs where the function changes from decreasing to increasing.

Step2: Analyze the graph

Looking at the graph of \(F(x)\), we can see that the function reaches a high - point (changes from increasing to decreasing) at \(x=- 1.2\), so there is a relative maximum at \(x = - 1.2\). The function reaches a low - point (changes from decreasing to increasing) at \(x = 1.2\), so there is a relative minimum at \(x=1.2\).

Answer:

C. \(F(x)\) has a relative maximum at \(x = - 1.2\) and a relative minimum at \(x = 1.2\)