Students will be able to justify where a function is increasing and decreasing, concave up and concave down. They will be able to justify a function’s extrema and inflection points. They will be able to apply the Extreme Value Theorem, the First Derivative Test, the Concavity Test, the Second Derivative Test, and the Mean Value Theorem. Students will be able to accurately sketch a curve given its derivative graph and sketch a curve’s derivative given its graph.
Students will be able to use the tangent line to approximate a function’s value. Students will be able to apply derivatives to position, velocity and acceleration algebraically, numerically and graphically. Students will be able to justify an optimization problem and explain a related rates problem.
Student version can be bought separately.