Unit 4: Applications of the Derivative

A. Extreme values

            1. Local (relative max / min) extrema

            2. Global (absolute max / min) extrema

B. Using the derivative

            1. Mean value theorem

            2. Rolle’s theorem

C.  Applying the first derivative

            1. Increasing and decreasing functions (slope of tangents)

            2.  Velocity

D.  Applying the second derivative

            1. Concavity

            2. Acceleration

E. Analysis of graphs using the first and second derivatives (curve sketching)

            1. Critical values

            2. First derivative test for extrema

            3. Concavity and points of inflection

            4. Second derivative test for extrema

            5.  Slant and horizontal asymptotes

            6.  End behavior

D. Optimization problems

E. Local linearization models

F. Related rates revisited

G. Particle motion

H. L’Hopital’s Rule