Calculus 1 — 20.2: Curve Sketching: f(x) = (x+2)(x−1)² скачать в хорошем качестве

Calculus 1 — 20.2: Curve Sketching: f(x) = (x+2)(x−1)²

Learn a repeatable seven-step system for sketching any polynomial by hand — no calculator needed. Working through f(x) = (x+2)(x−1)², this video walks from intercepts through both derivatives, a combined sign chart, and finally a complete, accurate graph with every key feature labeled and explained. Key concepts covered: • Finding x-intercepts using the zero product property and the y-intercept by direct substitution • Expanding a factored polynomial before differentiating to simplify the process • First derivative via the power rule: f'(x) = 3x² − 3 and finding critical numbers • Second derivative f''(x) = 6x and identifying possible inflection points • Building a combined sign chart — first derivative for increasing/decreasing, second derivative for concavity • Classifying critical points as relative maxima or minima using sign changes in f' • Confirming an inflection point by verifying a concavity change at x = 0 • Computing key point coordinates: relative max at (−1, 4), relative min at (1, 0), inflection at (0, 2) • Root multiplicity and graph behavior: odd multiplicity roots cross the axis, even multiplicity roots bounce • End behavior from the leading term x³ (negative infinity on the left, positive infinity on the right) • Tracing the final curve segment by segment, matching every portion to sign chart predictions ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Calculus 1 Lecture 3.6:  How to Sketch Gra...