Function Analysis Calculator – Extrema & Graph
Function analysis and graphing y = f(x)
Choose a standard function type, enter the coefficients, then see the domain, monotonicity, extrema, asymptotes, variation table and graph.
The calculator above studies a function completely: domain, derivative, intervals of increase and decrease, local extrema, asymptotes, the variation table, and the graph.
Formulas used
f′ > 0: increasing, f′ < 0: decreasing
f′(x₀) = 0 and f″(x₀) < 0 ⇒ local maximum
- Vertical asymptote x = a when f(x) → ±∞ as x → a.
- Horizontal asymptote y = L when f(x) → L as x → ±∞.
Worked example
For f(x) = x³ − 3x + 1, f′(x) = 3x² − 3 = 0 at x = ±1:
local max f(−1) = 3, local min f(1) = −1
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the function, for example x^3 − 3x + 1 or (2x + 1)/(x − 1).
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.