Skill: curve-sketching
Curve Sketching Calculator
Read a graph from its derivatives: f′ tells you where the curve climbs and falls, f″ tells you how it bends. Find critical points, classify them, locate inflection points, and sketch with confidence.
1 Curve analyzer
Enter a cubic f(x) = ax3 + bx2 + cx + d
(a ≠ 0) and get its critical points, classification, inflection point, and intervals of increase/decrease and concavity.
Steps
Enter coefficients and press Analyze.
2 Reading the output
- Critical points come from f′(x) = 0; each is labeled max, min, or neither.
- Increasing/decreasing intervals come from the sign of f′ between critical points.
- Concavity flips at the inflection point, where f′′ changes sign.