Unit 4: Contextual Applications of Differentiation

Unit 4 puts derivatives to work in real situations. You'll interpret a derivative's meaning and units in context ("rate of change of ___ with respect to ___ at time ___"), analyze straight-line motion with position, velocity, and acceleration (speeding up means velocity and acceleration share a sign), and solve related rates problems by writing an equation that links the quantities, differentiating with respect to time, and only then substituting values. The unit finishes with local linearity, using the tangent line to approximate function values and deciding whether that estimate is too big or too small from concavity, and L'Hospital's Rule for 0/0 and infinity/infinity limits. Always include units in context answers.