Section 2.1 – Average and Instantaneous Velocity.

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Presentation transcript:

Section 2.1 – Average and Instantaneous Velocity

VOCABULARY FIRST AVERAGE Velocity INSTANTANEOUS Velocity SPEED Slope of the secant line of a position function Slope of the tangent line Approximated using slope of secant line Found exactly using the first derivative The absolute value of velocity!!!

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

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

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

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 meters per hour at t = 5 hours.

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.

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

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