Question

(a) for what value(s) of x does the function obtain a relative minimum? (b) find the relative minimum value (c) for what value(s) of x does the function obtain a relative maximum? (d) find the relative maximum value (a) select the correct choice below and if necessary fill in the answer - box to complete your choice a. the function obtains a relative minimum at (type an integer or a decimal.) b. there is no solution

Explanation:

Step1: Analyze the graph

By observing the given graph of the function, we look for the points where the function changes from decreasing to increasing (for relative - minimum) and from increasing to decreasing (for relative - maximum).

Step2: Locate relative minimum

From the graph, we can see that the function changes from decreasing to increasing at \(x = 1\). So the function has a relative minimum at \(x = 1\).

Step3: Locate relative maximum

The function changes from increasing to decreasing at \(x=- 8\). So the function has a relative maximum at \(x=-8\).

Step4: Find relative maximum value

The \(y\) - value of the function at the relative - maximum point \((-8,8)\) is \(y = 8\).

Answer:

(a) A. The function obtains a relative minimum at \(1\)
(b) The relative minimum value is the \(y\) - value at \(x = 1\). From the graph, when \(x = 1\), \(y=-3\)
(c) The function obtains a relative maximum at \(-8\)
(d) The relative maximum value is \(8\)