1314L8 - Lesson 8 Some Applications of the Derivative...

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Lesson 8 – Some Applications of the Derivative 1 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 equation of the line tangent to 2 3 ) ( - = x x x f at the point 2 1 , 2 . Example 2: Find the equation of the line tangent to ) 1 7 ln( ) ( + = x x f when x = 2.
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2 Horizontal Tangent Lines, etc. Some other basic applications involve finding where the slope of the tangent line is equal to a given number. Example 3: Find all values of x for which the slope of the tangent line to x x x f ln 2 3 ) ( - = is horizontal. Example 4: Suppose 2 3 3 2 ) ( x x x f - = . Find all values of x for which 4 ) ( ' = x f . Note: In some cases you may need to use the quadratic formula to solve quadratic equations. a
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1314L8 - Lesson 8 Some Applications of the Derivative...

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