Lesson-8-filled

# Lesson-8-filled - Math 1314 Lesson 8 Some Applications of...

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Math 1314 Lesson 8 Some Applications of the Derivative Equations of Tangent Lines The first applications of the derivative involve finding the slope of the tangent line and writing equations of tangent lines. Example 1 : Find the slope of the line tangent to 15 5 ) ( 2 + - = x x x f at the point (2, 3). Example 2 : Find the equation of the line tangent to 2 2 4 ) ( x x x f - = at the point (3, -6).

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Example 3 : Find the equation of the line tangent to 2 3 2 5 ) ( x x x f - - = when . 2 = x Horizontal Tangent Lines, etc. Some other basic applications involve finding where the slope of the tangent line is equal to a given number. Example 4 : Find all values of x for which the line tangent to 9 4 4 ) ( 2 3 + + - = x x x x f is horizontal.
Example 5 : Find all values of x for which the slope of the line tangent to x x x f ln 2 3 ) ( - = is equal to 0. Example 6 : Find all values of x for which the slope of the line tangent to 7 5 4 ) ( 2 3 + - - = x x x x f is 3.

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Rates of Change Sometimes we re interested in finding the rate of change of a function at a specific point. Example 7
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Lesson-8-filled - Math 1314 Lesson 8 Some Applications of...

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