Definition of Derivative: Example 2

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In this video I go over example 2 on the definition of derivative. You can see example 1 in the video link below. In example 2, I solve the velocity and the speed of a function when given the distance or position function and solve it using the definition of derivative.


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Definition of Derivative: Example 2

Definition of Derivative Example 2.jpg

Example 1

(a) Find the derivative of the function:

f(x) = x2-8x + 9

(b) Find an equation of the tangent line to f(x) at the point (3, -6).

Example 2

The position of a particle is given by the equation of motion:

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where t is measured in seconds and s in meters. Find the velocity and the speed after 2 seconds.

Solution

image.png

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Speed = How fast you are going.
Velocity = How fast you are going and in what direction.

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