Final Exam Review
This exam will be worth 100 points and count 20% of your semester grade
Problems 1 Average rate of change and instantaneous rate of change
o Review problem #2 from exam 1.
o Additionally find the instantaneous rate of change at a point
by finding the value of the derivative at a point.
o Draw the tangent line at a point by applying the slope of the
tangent line found from the derivative.
Problem 2 Revenue, Cost and Profit functions
o Review problem #5 from exam 1
o Additionally find the marginal revenue, cost and profit
Problem 3 Equilibrium quantity and price
o Review problem #9 from exam 1
Problem 4 Retirement planning
o Review problem 4 from exam 2
o Additionally find the present value of a future amount
assuming a discount rate due to inflation.
Problem 5 Loan Amortization
o Review problem 9 from exam 2
Problem 6 Linear Programming
o Review problem 9 from exam 3 (an initial table will be
given) – you don’t have to show the graph but must list
corner points and show test.
Problem 7 Functions
o Find critical points
o Use second derivative test to determine relative maxima and
o Find the intervals where a function is increasing and
o Determine volume that produces maximum profit
o Determine maximum profit
Review Sec 10.1 #85 and 10.2 #95
Vocabulary / Concepts
Chapter 10 Vocabulary/Concepts: Absolute extrema Review all
Increasing / Decreasing function Critical number vocabulary/concepts
First derivative test Concavity from previous study
Relative maximum / minimum Intervals of Concavity guides.
Relative maxima / minima Inflection point
Relative extrema Second derivative test
Absolute maximum / minimum Absolute Extra