Change

Part III: Moving — Chapters 8, 9, 10 — Plane Position: (0, -0.2) radius 0.4 — 58 Primitives

Workflow

1. Verify continuity at the point or interval of interest — confirm the function meets the three conditions (defined, limit exists, limit equals value)
2. Compute derivatives using the appropriate rule (power, chain, product, quotient) to find rates of change
3. Find critical points where f'(x) = 0 or f'(x) is undefined, then classify using the first or second derivative test
4. Integrate using antiderivatives and the Fundamental Theorem of Calculus to accumulate quantities
5. Solve ODEs by identifying the equation type and applying the matching technique (separation, integrating factor, etc.)

Key Concepts

Derivative (definition): The derivative of f at x is f'(x) = lim_{h->0} [f(x+h) - f(x)]/h, when this limit exists. It represents the instantaneous rate of change of f at x, and the slope of the tangent line to the graph at (x, f(x)).

• computing the instantaneous rate of change of a quantity
• finding the slope of a curve at a specific point