Programmers and Teachers:
Critical Points Calculator
Critical Points Lesson
What are Critical Points?
A critical point is a point on a given domain of a function where the function’s derivative is either zero or undefined, and the function itself exists at that point.
How to Find the Critical Points of a Function?
Critical points x = c are found under the following conditions:
1.) f ‘(c) equals zero OR f ‘(c) is undefined
2.) f(c) exists
Where c is the critical point that satisfies both conditions, f ‘(c) is the derivative of the input function f(x) evaluated at x = c, and f(c) is the input function f(x) evaluated at x = c.
Steps for finding the critical points of a given function f(x):
1.) Take derivative of f(x) to get f ‘(x)
2.) Find x values where f ‘(x) = 0 and/or where f ‘(x) is undefined
3.) Plug the values obtained from step 2 into f(x) to test whether or not the function exists for the values found in step 2
4.) The x values found in step 2 where f(x) does exist can be taken as critical points since the function exists at these points and they lie within the domain of our function f(x)
Example Problem 1
Example Problem 2
How the Calculator Works
CSS is then used to provide custom styling to the calculator and answer elements so that it is easy to read and use as needed. Everything from the clickable calculator button styling to the automated scroll bars in the solution field are styled using CSS.