Section 3.1 slides

# Section 3.1 slides - • Definition of the Derivative of a...

This preview shows pages 1–15. Sign up to view the full content.

Assignment 4 Section 3.1 The Derivative and Tangent Line Problem

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

View Full Document
The Basic Question is… How do you find the equation of a line that is tangent to a function y=f(x) at an arbitrary point P? To find the equation of a line you need: a point and a slope
How do you find the slope when the line is a tangent line?

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

View Full Document
First, we approximate with the secant line. h x f h x f m ) ( ) ( sec - + =
How do we make the approximation better? Choose h smaller… And smaller… And smaller… And smaller… How close to zero can it get? Infinitely

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

View Full Document
Definition of slope of the tangent line If f(x) is defined on an open interval (a,b) then the slope of the tangent line to the graph of y=f(x) at an arbitrary point (x,f(x)) is given by: h x f h x f m h ) ( ) ( lim 0 - + =
Example: #6—Find the slope of the tangent line to the graph of the function at the given point. (-2, -2) 2 5 ) ( x x g - =

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

View Full Document
The limit that is the slope of the tangent line is actually much more. .

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • Definition of the Derivative of a Function The derivative of f at x is given by Provided the limit exists. For all x for which the limit exists, is a function of x. h x f h x f x f h ) ( ) ( lim ) ( '-+ = → ' f Notations for derivative ] [ )] ( [ ' ) ( ' y D x f dx d y dx dy x f x Find the derivative by the limit process. #20 #24 2 3 ) ( x x x f + = x x f 4 ) ( = Find an equation of the tangent line to th graph of f at the given point. • #26 » ( - 3, 4) 1 2 ) ( 2 + + = x x x f #34 Find an equation of the line that is tangent to the graph of f and parallel to the given line. 2 ) ( 3 + = x x f 4 3 =--y x Sketch the graph of f’ #46 What destroys the derivative at a point? a) Cusps b) Corners c) Vertical tangents And… Points of Discontinuity Fact: If a function is differentiable at x=c, then f is continuous at x=c...
View Full Document

{[ snackBarMessage ]}

### Page1 / 15

Section 3.1 slides - • Definition of the Derivative of a...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online