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

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
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?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 10 2 Slope of a Curve at a point Slope of a curve at a point measures
Background image of page 2
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:
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 10 6 2) What is the equation of the tangent line to f ( x ) = 1 x + 1 at x = 3?
Background image of page 6
Lecture 10 7 Find the slope of the tangent line to
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 12

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

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online