TANGENT LINES Notes 2.4 – Rates of Change. I. Average Rate of Change A.) Def.- The average rate of change of f(x) on the interval [a, b] is.

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Presentation transcript:

TANGENT LINES Notes 2.4 – Rates of Change

I. Average Rate of Change A.) Def.- The average rate of change of f(x) on the interval [a, b] is

B.) Ex.- Find the average rate of change of f(x) on [2, 5] for the following functions: as x changes from 2 to 5, the y-values increase at an average rate of 7 to 1.

C.) Def.- The average rate of change of f(x) on the interval [a, a+h] is a f(a) a+h f(a+h)

II. Instantaneous Rate of Change A.) Def.- The instantaneous rate of change of f(x) at x =a (if it exists) is

A.) Find the instantaneous rate of change of the following functions at the given x values. Then, give the equation of the tangent line at that point. III. Examples

Tangent line –

IV. Normal Line A.) Def. – The normal line to a curve at a point is the line perpendicular to the tangent line at that point. B.) Ex. – Find the equation of the normal line to the following graph:

V. Free Fall Motion A.) B.) A rock is dropped from a cliff 1,024’ high. Answer the following: 1.) Find the average velocity at t = 3 seconds.

2.) Find the instantaneous velocity at t = 3 seconds.

3.) Find the velocity at the instant the rock hits the ground.