Interpreting derivatives in context and straight-line motion

Learning objectives

Interpret the value of a derivative at a point as an instantaneous rate of change in context, stating the correct units (units of output per unit of input) and explaining the meaning in a full sentence

Relate the position, velocity and acceleration of a particle moving along a line: velocity is the derivative of position and acceleration is the derivative of velocity, and evaluate each from a formula, a table or a graph

Determine when a particle is moving left or right, is at rest or changes direction from the sign of velocity, and calculate speed as the absolute value of velocity

Decide whether a particle is speeding up or slowing down by comparing the signs of velocity and acceleration, and justify the conclusion

Analyze rates of change in applied contexts other than motion, such as the rate of change of a volume, a population or a cost, and interpret the sign and size of the derivative