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Section 2.1 – Average and Instantaneous Velocity

Section 2.1 – Average and Instantaneous Velocity. VOCABULARY FIRST. AVERAGE Velocity. Slope of the secant line of a position function. INSTANTANEOUS Velocity. Slope of the tangent line Approximated using slope of secant line Found exactly using the first derivative. SPEED.

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Section 2.1 – Average and Instantaneous Velocity

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  1. Section 2.1 – Average and Instantaneous Velocity

  2. VOCABULARY FIRST AVERAGE Velocity • Slope of the secant line of a position function 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. f(x+h) x x+h f(x) Given the curve:

  4. NUMERICALLY A. Find the average velocity over the interval 1 < t < 3. B. Using appropriate units, explain the meaning of your answer. 0.9 represents the average meters per hour of a particle from t = 1 hour to t = 3 hours

  5. NUMERICALLY A. Find the average velocity over the interval 0 < t < 4 B. Using appropriate units, explain the meaning of your answer. 1.25 represents the average meters per hour of a particle from t = 0 to t = 4 hours

  6. NUMERICALLY A. Estimate the velocity at t = 5. Note: velocity implies INSTANTANEOUS velocity B. Using appropriate units, explain the meaning of your answer. The velocity is approximately 0.733 meters per hour at t = 5 hours.

  7. 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

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

  9. 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. Find the average rate of change of the function over the interval –3 < x < -1.

  10. Section 2.2 Average and Instantaneous Rate of Change The Derivative of a Function at a Point

  11. Given the graph of f below on [-10,9], where does f ‘ (x) NOT exist? X X X X X X X X X

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