Calculus in 10 Minutes or Less

1. Calculus in 10 Minutes or Less

2. Slope position time

3. Slope position tangent! time

4. Derivatives • Derivatives are the slope of a function at a point • Slope of x vs. t • velocity - describes how position changes over time • Slope of v vs. t • acceleration - describes how velocity changes over time • Slope of a vs. t • jerk - describes how acceleration changes over time

5. Derivatives

6. Derivative Rules

7. If the position of an object is described by the function What are the velocity and acceleration functions?

8. Area velocity Easy! time

9. Area velocity Harder!!! time

10. Integrals • Integrals are anti-derivatives • Graphically, integrals are the area under a curve • Area under a v vs. t graph = Displacement

11. Integrals

12. Integral Rules

13. An object’s acceleration is described by a(t) = 2t. Find the velocity and position functions.

14. Initial Conditions If x = 5 when t = 0, what is the displacement function for this velocity function? -so- -so-

15. Definite Integrals • Taking the integral from one point to another. • Same rules apply, but don’t have to do “+C”

16. Find the displacement from t = 2 seconds to t = 4 seconds for the velocity function