Chapter 6 Review New Concepts ● ● ● ● Implicit Differentiation Mean Value Theorem for Integrals Mean Value Theorem for Derivatives Improper Integrals ● Distance/Velocity/Acceleration Functions ○ Determine initial values ○ Determine height at any time Optimization ○ Use math language when solving ○ Apply either 1st or 2nd derivative test Finding Derivatives (Rules) ○ Power ○ Product ○ Quotient ○ Chain ○ Trig ○ Combine all rules together :-) FTC - Chain Rule Extension ○ Review FTC for derivative or integral and integral of derivative Applying L’Hopital’s Rule ● ● ● ● Review Concepts ● ● ● ● ● ● ● ● ● ● Distance v Time graphs and Velocity v Time Evaluate limits Define Continuity using limits Define Differentiability using limits Definition of Derivative Compare f(x), f’(x), f”(x). Use derivatives to describe a function (using increasing, decreasing, max, min and concavity) Integral “Rules” and properties for writing as a single integral Translating integrals ○ +k adds a rectangle ○ -h must shift bounds with equation Fundamental Theorem of Calculus ○ Part 2 F(b)-F(a) ○ Part 1 derivative of integral & integral of derivative (Definite and Indefinite) Area between two curves ○ Vertical ○ Horizontal