Function Calculator

Basic function calculation and graphing; supports analysis and extrema

Function Settings

Function Expression f(x) =

Supported: +, -, *, /, ^, sin, cos, tan, log, sqrt, abs, pi, e

X Minimum

X Maximum

Calculation Step

Function Examples

Function Graph

Enter function expression and set domain to start analysis

Function Analysis Knowledge

Critical Points

Critical points are where the derivative is zero or undefined, including local maxima, minima, and inflection points. These points are crucial for understanding function behavior.

Monotonicity

A function is increasing where the derivative is positive and decreasing where the derivative is negative.

Concavity

A function is concave up where the second derivative is positive and concave down where it is negative.

Numerical Differentiation

This calculator uses numerical differentiation to approximate derivatives; useful for complex functions that can't be differentiated analytically.