- Algebra Calculator
- Practice
- Lessons
- Pricing
- Log In
- Sign Up
Absolute Value Equation Calculator
What do you want to calculate?
Example: 3|2x+1|+4=25
Example (Click to try)
3|2x+1|+4=25
About absolute value equations
Solve an absolute value equation using the following steps:
- Get the absolve value expression by itself.
- Set up two equations and solve them separately.
Absolute Value Equation Video Lesson
- Khan Academy Video: Absolute Value Equations
Need more problem types? Try MathPapa Algebra Calculator
Close Ad
Clear Absolute Value Equation Calculator »
What is Absolute Extrema?
It refers to the most extensive and smallest values of a function. For instance, the highest profit a company can make, the least quantity of cement needed to complete a building, and much more. Knowing how to find absolute extrema of a function is a daunting task to many students. In order to make the process easier for you, we've prepared this calculator - feel free to use it online.
How To Use The Absolute Extrema Calculator
Finding the absolute extrema is very easy with our calculator. All you need to do is to:
- Identify the critical numbers, and
- Enter them into the function on the calculator
- As simple as that, and you have your answer!
However, are you aware that there is a way to find absolute extrema without a calculator?
So first, let us look at some of the comparisons of absolute extrema.
Local vs. Absolute Extrema
An absolute maximum occurs at the x value where the function is the biggest. In contrast, a local maximum occurs at an x value if the function is more prominent than points around it (i.e., an open interval around it).
A local minimum occurs at an x value if the function is smaller than the points around it. In contrast, an absolute minimum occurs at the x value where the function is the smallest (i.e., an open interval around it).
Absolute vs. Relative Extrema
The absolute extrema will refer to the absolute minimums and maximums, while the relative extrema will refer to the relative minimums and maximums. Note that relative extrema do not occur at the endpoints of a domain. Unlike the absolute extrema, they only occur interior to the domain.
Formula For Absolute Extrema Calculator With Interval
For absolute extrema, we should first have a continuous function, f(x), on an interval [a, b]. Therefore, using the function, we can be able to find the absolute extrema in the following steps:
- First, verify that the function is continuous
- Then find all the critical points of f(x) that are in the interval [a, b]
- Evaluate the function at the critical points derived from step 2 and the endpoints
- Finally, identify the absolute extrema
You can see that the procedure above does not take much professional writing help. Provided you have the critical points and evaluate them, finding the absolute extrema becomes easy-peasy.
Now, there are other ways of finding the absolute extrema:
How To Find the Absolute Extrema of the Function on the Closed Interval Calculator
Using this method requires you to compute a derivative. Below is how to go about this process:
- Identify all critical numbers of f within the interval i.e. f'(x) = 0,
- Solve for x
- Consider only those solutions of x that satisfy a ≤ x ≤ b.
- Enter the values into the function f(x).
- Enter the endpoints, a and b, into the function f(x).
The immense value becomes the absolute maximum from the results you get, while the smallest value becomes the absolute minimum. You can use the absolute extrema calculator on interval to arrive at your answer.
How To Find Absolute Extrema on a Graphing
Once you’ve found all the critical numbers of f within the interval [a, b], you can move on to plug the values on your graph paper. Draw the graph to arrive at your absolute minimum and maximum points.
Example:
Find the absolute extrema for:
g (t)=2t3+3t2−12t+4 on [−4,2]
Solution:
g′ (t) =6t2+6t−12=6(t+2) (t−1)
t = −2 and t = 1
Therefore:
g (-2) = 24
g (-4) = -28
g (1) = -3
g (2) = 8
Pay Someone To Do My Math
Are you saying, “I want somebody to do my math homework for me?” We offer professional help with math homework at cheap rates.
Try our expert online service today!
Extremum of a Function
- Mathematics
- Functions
- Extremum of a Function
Absolute Extremum Calculator
Local/Relative Maximum Calculator
Local/Relative Minimum Calculator
Answers to Questions (FAQ)
How to calculate a extremum?
To find the extreme values of a function (the highest or lowest points on the interval where the function is defined), first calculate the derivative of the function and make a study of sign.
An extremum of a function is reached when it's derivative is equal to zero and changes of sign.
A minimum of a function $ m $ (lowercase m) exists when, for all $ x $, $ f(x) >= m $ is greater than or equal to a minimum $ m $.
Example: Find the extremum of the polynomial $ f(x) = x^2 $ defined over $ \mathbb{R} $: the function has a minimum in $ x=0 $ and $ f(x) >= 0 $ over its domain of definition $ \mathbb{R} $.
A maximum of a function $ M $ (uppercase M) exists when for all $ x $, $ f(x) <= M $ is less than or equal to the maximum.
What is the difference between a relative/local extremum and an absolute/global extremum?
An extremum of a function is necessarily defined on an interval. If the interval is the entire domain of definition of the function then it is a global/absolute extremum, otherwise it is a local/relative extremum.
How to determinate the number of extremum?
A function always has 2 global extrema, a maximum and a minimum.
for a constant function the minimum and the maximum are identical.
The number of local extremums depends on the function, but for a polynomial of degree $ n $, there are, at most, $ n-1 $ local extremums.
Example: The polynomial of degree 2 $ x ^ 2 $ has $ 1 $ local minimum in $ x = 0 $
What does extrema mean?
Extrema is the plural form of extremum (from latin, meaning Extremity).
Source code
dCode retains ownership of the "Extremum of a Function" source code. Except explicit open source licence (indicated Creative Commons / free), the "Extremum of a Function" algorithm, the applet or snippet (converter, solver,
encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Extremum of a Function" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Extremum of a Function" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Extremum of a Function" or any of its results, is allowed as long as you cite dCode!
Cite as source (bibliography):
Extremum of a Function on dCode.fr [online website], retrieved on 2022-11-24, //www.dcode.fr/extremum-function