Definition: Related rates problems involve finding one rate of change when another related rate of change is known.

Highlight: The systematic approach to solving related rates step by step involves drawing pictures, listing known quantities, establishing relationships, and proper differentiation.

Example: When using local linearity for approximation, concave up functions lead to underestimates, while concave down functions result in overestimates.

Quote: "Substituting a non-constant quantity before differentiating is NOT allowed!"

Definition: The derivative represents the rate of change of one quantity with respect to another, with units expressed as the ratio of dependent to independent variable units.

Example: In motion analysis, position s$t$ is measured in feet, velocity s'$t$ in feet/second, and acceleration s''$t$ in feet/second².

Highlight: The sign of the derivative provides crucial information about the behavior of a function - positive derivatives indicate increase, while negative derivatives indicate decrease.

Vocabulary: Displacement refers to the net change in position, distinct from the total distance traveled.