Curve Discussion
Math · free browser app
Roots, extrema, inflection points and derivatives — the classic Kurvendiskussion, drawn live.
Description
Type a function f(x) and get the classic full curve discussion, drawn instead of just listed: roots, maxima and minima, inflection points, symmetry, monotonicity and the first two derivatives. Sine, cosine, exponential, logarithm, square root and powers are all understood — implicit products like 3x work too.
Preset families from a straight line to a rational function with a pole come with sliders for their coefficients, so you can watch every marker move as the curve changes; the analysis runs on the plotting interval you choose. The classic school exercise, made visual.
Examples
The classic cubic: x³ − 3x
The default example. The app marks the roots at 0 and ±√3, the maximum at (−1, 2), the minimum at (1, −2) and the inflection point at the origin — and shows how f′ and f″ predict each of them.
A pole: (x² − 1)/(x + 2)
The rational preset. At x = −2 the denominator vanishes: the app draws the vertical asymptote and the two branches, finds the roots at ±1 and one extremum on each side of the pole.
Symmetry: a sine wave
Pick the sine preset a·sin(bx + c): with c = 0 the curve is odd — point-symmetric about the origin — and every root, extremum and inflection point repeats with period 2π/b. Shift c and watch the symmetry verdict change.