What this calculator offers
- Parses expressions safely with a Shunting-yard evaluator and plots up to three functions in different colors.
- Detects x-intercepts and intersections by scanning for sign changes, then converging with bisection.
- Identifies extrema via numeric derivatives: f′ brackets the critical point, f″ classifies minima and maxima.
- Encodes inputs, range, and options in the URL so you can share the same view and reproduce the full step log.
For educational use only. Verify the formulas and ranges before relying on the results.
Set up your functions and range
- Pick a preset (or type your own functions).
- Zoom/pan in the graph preview to explore.
- Use “Detected points” to jump to intercepts, intersections, and extrema.
Graph preview
Move the pointer over the canvas to inspect coordinates.
Keyboard shortcuts: arrows pan, +/- zoom, F fits the Y range, R resets the viewport.
Detected points
Points detected: 0
How it's calculated
Teacher notes
- The step log records each bracket, interval width, and g(x) value so students can follow the bisection workflow.
- Extrema rely on f′ sign changes and the sign of f″, making it easy to connect the numeric method to calculus concepts.
- Canvas controls work with mouse, touch, and keyboard, ensuring the same graph can be reproduced in class or online.
FAQ
How does the calculator find intersections or x-intercepts?
The viewport is sampled at fixed intervals to detect sign changes. Each bracket is refined with up to 40 bisection iterations, and the step-by-step log lists the interval width and g(x) values so you can follow the convergence.
What happens when I switch between degrees and radians?
Trigonometric expressions are converted internally according to the selected unit. Choosing degrees makes sin(90) evaluate to 1, while radians expects values such as sin(pi/2), so the graph remains correctly scaled.