1. Applications of Derivatives Flash Cards

2. Absolute Extrema(Max and Min)

3. Absolute Extrema:MUST BE WITHIN A CONTINUOUS INTERVALABS max: the highest point the graph reaches ABS min: the lowest point the graph reaches

4. Local Extema(Max and Min)

5. Local ExtremaTHERE CAN BE AN INFINITE NUMBER OF LOCAL MAXS/MINSLocal max: the highest point the graph reaches where the slope of the line equals zeroLocal min: the lowest point the graph reaches where the slope of the line equals zero

6. Position, Velocity, Acceleration(relationships)

7. s”(t) = v’(t) = a(t)

8. Related Rates(steps)

10. X =

11. C =dc dt dy dt C Y dx dt X Use the Pythagorean theorem to find the missing variable: X2 + Y2 = C2 Use the derivative of the Pythagorean theorem to find the missing variable: 2x dx + 2y dy = 2c dc dtdtdt

12. Optimization(steps)

13. 1. Find 2 equations that correspond with the problem [one equation will be a substitution equation (the variable found will be substituted into the other equation), and the other will be minimized or maximized].2. Solve for one variable (in the substitution equation) and plug that into the maximized/minimized equation(answer will have a variable in it).3. Take the derivative of the minimized/maximized equation (simplify before if possible).4. Set the derivative equal to zero and solve for the variable (will be an actual value). That’s your answer!