Answer:
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:
- the height of the point in the trough on the left
- 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