Calculus grapher – f, f′, f″ and the antiderivative
MathematicsCalculusAges 17–18
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Sign in to playDrag to reshape the graph of f(x) with the hill, triangle, parabola, sine, freehand, shift and tilt tools, and watch the graphs of the derivative f′(x), the second derivative f″(x) and the antiderivative F(x) = C + the integral of f from x₀ update instantly. A reference line shows the tangent line, the values of f, f′ and F and the shaded area; a practice screen lets students sketch their prediction of f′ or F and compare it with the answer. Based on the "Calculus Grapher" simulation by PhET Interactive Simulations, University of Colorado Boulder (CC BY 4.0); rewritten.
Lesson: Antiderivatives
How to use
Parameters you can change
- Screen Derivative, Integral, Advanced, Prediction practice
- Starting function A single hill, f = 0, f = sin x, f = x²
- Graph-bending tool Hill, Triangle, Parabola, Sine wave, Freehand, Shift up/down, Tilt
- Tool width σ 0.3–3
- Integral starting point x₀ -6–6
- Antiderivative constant C -3–3
- Show second derivative f″ graph
- Show reference line
- Show tangent line
- Shade area from x₀ to a
