Skill: curve-sketching
Curve Sketching Tutor Help
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 Concept recap
The essentials of Curve Sketching with Derivatives, on one screen.
f′ Up / down
f′ > 0 → increasing; f′ < 0 → decreasing. Critical points (f′ = 0 or undefined) are the only max/min candidates.
f′′ Bend
f′′ > 0 → concave up; f′′ < 0 → concave down. Inflection = concavity flip (f′′ = 0 plus sign change).
Classify
First-derivative test (sign change of f′) or second-derivative test (sign of f′′). A critical point with no sign change is neither.
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