Question

use the graph of the function f given below to answer the questions. is there a local minimum at x = 4? yes no 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: Recall the definition of local minimum

A local minimum of a function \(y = f(x)\) is a point \((a,f(a))\) such that \(f(a)\leq f(x)\) for all \(x\) in some open interval containing \(a\).

Step2: Analyze the graph at \(x = 4\)

Looking at the graph, we can see that at \(x = 4\), the function has a point where the \(y -\)value is lower than the \(y -\)values of the points in the immediate neighborhood of \(x = 4\).

Answer:

A. The local minimum is \(y=-16\)