Critical Number Calculator
Find critical numbers of a function f(x) by computing its derivative and solving f'(x)=0. Enter a function using standard notation (e.g., x^3 - 3*x^2 + 1).
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Critical Number Calculator
- Enter your function in the f(x) field. Use
^for exponents,*for multiplication. Example:x^3 - 3*x^2 + 1. - Click "Find Critical Numbers" to compute.
- View results below: critical numbers (x-values where derivative is zero or undefined) appear in green. If none are found in the range [-10, 10], a warning is shown.
- Note: The calculator uses numerical approximation (bisection method) for derivatives, so results are approximate to 6 decimal places.
Tips:
- Use standard math functions:
sin(x),cos(x),sqrt(x),log(x)(natural log),abs(x),exp(x). - Avoid division by zero or functions undefined at x=0 (e.g.,
1/x). - The calculator searches for critical numbers only between x = -10 and x = 10.
Previous Results
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Frequently Asked Questions
A critical number of a function f(x) is a value x = c in its domain where f'(c) = 0 or f'(c) does not exist.
It numerically approximates the derivative and uses the bisection method to find roots of f'(x)=0 within the range [-10, 10].
You can use standard arithmetic, ^ for exponent, and functions like sin, cos, tan, log, sqrt, abs, exp. Use * for multiplication.
