1. Section 2.1 – Average and Instantaneous Velocity

2. VOCABULARY FIRST
AVERAGE Velocity
Slope of the Secant Line
INSTANTANEOUS Velocity
Slope of the Tangent Line
Approximated using slope of secant line
Found exactly using the first derivative
SPEED
The absolute value of velocity!!!

3. Given the curve:
f(x+h)
x+h x
f(x)

4. NUMERICALLY
Find the average velocity over the interval 1 < t < 3.
Find the average velocity over the interval 0 < t < 4
Estimate the velocity at t = 5.
Note: velocity implies INSTANTANEOUS velocity

5. GRAPHICALLY
Find the average rate of change of f(x) on [-2, 2]
Estimate the instantaneous rate of change of f(x) at x = 0

6. Find the average velocity of the ship in the first two hours
Estimate the velocity of the ship after 75 minutes

7. Find the average rate of change of the function
over the interval –3 < x < -1.
Find the average rate of change of the function
over the interval [1, 9].
Find the average rate of change of the function
over the interval [1, 3], rounding to three decimal places.