Question

Here’s is a graph of the function f.

Use the graph to find the following.
If there is more than one answer, separate them with commas

Answer 1

The local minima are 1 and -2

The values at which the function f has a local minimum are -3 and 4

Explanation:

Main Concepts:

Brief side-discussion about local vs global minimums

Concept 1. What a Local minimum is

Concept 2. Where a local minimum is at

Brief side-discussion: a Local minimum vs Absolute or Global minimum

A local minimum is the height of any "low" point on a continuous section of the function where all of the points "near" it are higher.

In contrast, an Absolute minimum (sometimes called a "global minimum"), is the lowest height the function ever reaches.

Concept 1. What a Local minimum is

This problem is asking about local minimums, of which there are two:

1. the height of the point in the trough on the left
2. the height of the point in the trough on the right

"The Local minimum value" itself IS the height of the point (the "y"-value).

The point on the left has coordinates (-3,1), and the point on the right has coordinates (4,-2).

So, the local minima are 1 and -2

Concept 2. Where a local minimum is at

The minima are different from "The values AT which the function has a local minimum" which is the input (or, "x"-value) that will produce that output when put into the function.

So, the values at which the function f has a local minimum are -3 and 4