Derivatives Lesson Oct 5
- 2. You drive a car for 2 hours and travel 90 km. What is your average velocity? distance rate = time 90 = 2 = 45 km/hr
- 3. 100 B distance (km) 50 A 1 2 time (hrs)
- 4. 100 B f(2) f(1) = distance traveled distance (km) 50 A 2 1 = time elapsed 1 2 time (hrs)
- 5. Average velocity between points A and point B? distance traveled AV = time elapsed rise = run = slope of line AB
- 6. In general: The average velocity over any interval is the slope of the line joining the endpoints of the interval. This line is called a secant line.
- 7. B f(a +h) f(a) distance A h a a + h time f(a+h) f(a) average velocity = h
- 8. B B f(a +h) f(a) distance B A tangent line a a + h time
- 9. Instantaneous Velocity ( at t = a ) lim f(a + h) f(a) = h 0 h This limiting value is the slope of the tangent line to the curve at point A as the time interval gets shorter.
- 12. Attachments Beach Buddies by rcktmanil