What this calculator offers
- Parses expressions safely with a Shunting-یارڈ 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 ان پٹ اقدار, range, and options in the URL so you can شیئر کریں the same view and reproduce the full step log.
For educational use only. Verify the formulas and ranges before relying on the نتائج.
Set up your functions and range
Detected points
Points detected: 0
حساب کیسے کیا گیا
گراف منظر
نقاط دیکھنے کے لیے پوائنٹر کو کینوس پر حرکت دیں۔
کی بورڈ شارٹ کٹس: تیر منظر کھسکاتے ہیں، +/- سے زوم ہوتا ہے، F سے Y رینج فٹ ہوتی ہے، اور R منظر کو ری سیٹ کرتا ہے۔
استاد کے نوٹس
- 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.
عمومی سوالات
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 مرحلہ وار 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.