lecture10

# lecture10 - f ( x ) = − 3 x − 2 at any point ( x, f ( x...

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Lecture 10 1 Lecture 10: (Sec. 2.6) The Derivative of a Function A machine de- preciates linearly over nine years of its useful life. Let V represent the value of the machine at the end of year t . If the function modeling that relationship is V = 1250 t + 12 , 750, a) what is the selling price of the machine? b) what does the slope of the line represent?

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Lecture 10 2 Slope of a Curve at a point Slope of a curve at a point measures
Lecture 10 3 To fnd the slope oF a curve at a point : Slope of the secant line : Now Fnd the slope of the secant line for the following:

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Lecture 10 4 Slope of the tangent line to the graph of y = f ( x ) at ( x, f ( x )): We have the following result:
Lecture 10 5 ex. 1) Find the slope of the tangent line to f ( x ) = 1 x + 1 at any point ( x, f ( x )).

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Lecture 10 6 2) What is the equation of the tangent line to f ( x ) = 1 x + 1 at x = 3?
Lecture 10 7 Find the slope of the tangent line to

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Unformatted text preview: f ( x ) = − 3 x − 2 at any point ( x, f ( x )). NOTE: Lecture 10 8 The Derivative of a Function Given a function y = f ( x ). The derivative of y with respect to x is the function f ′ deFned by: f ′ ( x ) = The domain of f ′ ( x ): ex. If f ( x ) = 1 x + 1 , then f ′ ( x ) = What is the domain of f ′ ? Lecture 10 9 Notation for the Derivative Given y = f ( x ), we write Lecture 10 10 1) Find f ′ ( x ) for f ( x ) = √ x − 2. Lecture 10 11 2) Write the equation of the tangent line to f ( x ) = √ x − 2 at x = 6. Lecture 10 12 (Master it question:) Find the x-values of all points at which the tangent line to f ( x ) = 1 x + 1 is parallel to x +9 y − 6 = 0. Write the equation of one of those lines....
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## This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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lecture10 - f ( x ) = − 3 x − 2 at any point ( x, f ( x...

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