[
  {
    "term": "context",
    "definition": "A contextual derivative statement must identify the input, output, instant, units, and practical meaning. Positive and negative values describe direction of change, not whether the quantity itself is positive."
  },
  {
    "term": "linearization",
    "definition": "Linearization uses the tangent line as a nearby approximation. Accuracy improves near the center point and depends on curvature and input distance."
  },
  {
    "term": "motion",
    "definition": "Position, velocity, and acceleration are successive layers of change. Their signs and zeros describe direction, speed changes, turning, and concavity, while their units distinguish the quantities."
  },
  {
    "term": "related",
    "definition": "Related-rates problems connect quantities that change together. An equation describes the geometric or physical relationship; differentiating with respect to time turns that relation into a rate equation."
  }
]