mfe-changelisted

# 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 **Definite Integral** (definition): The definite integral of f from a to b is integral_a^b f(x)dx = lim_{n->inf} sum_{i=1}^{n} f(x_i*)*Delta_x, when this limit exists. It represents the signed area between f and the x-axis over [a,b]. - computing the total accumulation of a quantity over an interval - finding the area enclosed between a curve and the x-axis **Ordinary Differential Equ