Define the derivatives of a function. Relate the derivative to instantaneous rate of change. Relate the derivative to the concept of tangency. In Stage 6, we investigate the problem of computing derivatives. In later Stages, we will consider a rich variety of applications of the derivative.
Objectives Use the definition of differentiability.
Formulate a limit problem to investigate the differentiability status of a given function at a given point. Determine whether a given function is differentiable at a given point. Distinguish between continuity and differentiability. Determine and instantaneous rates of change of a function. Go to the Practice area to develop skills and understanding.