Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) y= fix) absolute maximum value absolute minimum value local maximum value(s) local minimum value(s)
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![**Instructions for Students:**
Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
**Graph Description:**
The given graph displays the function \(y = f(x)\), plotted on a grid. The x-axis ranges from 0 to 3, and the y-axis ranges from -1 to 1. The curve appears to oscillate within these bounds.
**Function Analysis:**
- **Absolute Maximum Value:**
Identify the highest point on the graph and record the y-value.
- **Absolute Minimum Value:**
Identify the lowest point on the graph and record the y-value.
- **Local Maximum Values:**
Determine the peak points within specific intervals excluding the endpoints if they are not the highest overall.
- **Local Minimum Values:**
Determine the trough points within specific intervals excluding the endpoints if they are not the lowest overall.
**Input Fields:**
- Absolute Maximum Value: [_______]
- Absolute Minimum Value: [_______]
- Local Maximum Value(s): [_______]
- Local Minimum Value(s): [_______]
**Note:** Use the graph provided to fill in the boxes with the corresponding values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d9375f8-7e1c-499e-addd-7f9edafd655a%2Fc4238887-77f2-4dba-9112-6cd4f264dbb1%2F1jrxha_processed.jpeg&w=3840&q=75)
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