Section 2.1 – Average and Instantaneous Velocity

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Presentation transcript:

Section 2.1 – Average and Instantaneous Velocity

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!!!

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

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

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

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

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.