Question

use the graph of the function f given to answer the questions.
if there is a local minimum at x = 4, what is it? select the correct choice below and fill in any answer boxes within your choice.
a. the local minimum is y =
(type an integer.)
b. there is no local minimum at x = 4.

Explanation:

Step1: Understand Local Minimum

A local minimum of a function is a point where the function value is less than or equal to the values of the function in its immediate neighborhood. From the graph, we need to check the y - value at \(x = 4\).

Step2: Analyze the Graph

Looking at the graph, the lowest point (local minimum) seems to be at \(x=4\) (or around that x - value). From the grid, we can observe that the y - coordinate of the local minimum (the bottom of the "valley" in the graph) is \(- 16\) (assuming the grid lines and the scale, since the graph has a minimum point which we can infer from the visual. If we look at the graph, the local minimum occurs at \(x = 4\) (or the x - value corresponding to the minimum point) and the y - value is \(-16\).

Answer:

The local minimum is \(y=\boxed{-16}\)