Differentiablilty & Equation of Tangent Line

Differentiablilty & Equation of Tangent Line - -3 x ( x-4)...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Where is a function not differentiable Equation of a Tangent line
Background image of page 1

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

View Full DocumentRight Arrow Icon
1) A function f ( x ) is not differentiable at a point x = a , if there is a “corner” (or sharp point) at a . Where a Function is Not Differentiable :
Background image of page 2
2) A function f ( x ) is not differentiable at a point x = a , if there is a vertical tangent at a . Where a Function is Not Differentiable:
Background image of page 3

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

View Full DocumentRight Arrow Icon
3) A function f ( x ) is not differentiable at a point x = a , if it is not continuous at a . Example: g ( x ) is not continuous at –2, so g ( x ) is not differentiable at x = –2. Where a Function is Not Differentiable:
Background image of page 4
Find the points on the graph of f at which the tangent line is horizontal.
Background image of page 5

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

View Full DocumentRight Arrow Icon
Recall that: the derivative is the slope of the tangent line the slope of a horizontal line is 0. Therefore, we wish to find all the points on the graph of f where the derivative of f equals 0.
Background image of page 6
First find the derivative of f: f ( x ) = - 3 x 3 - 1 + 6 2 x 2 - 1 f ( x ) = - 3 x 2 + 12 x Find points at which the tangent line to is horizontal. f ( x ) = - x 3 + 6 x 2
Background image of page 7

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

View Full DocumentRight Arrow Icon
Then find where m = 0 by setting To obtain ( 29 0 f x = - 3 x 2 + 12 x =
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
Background image of page 13

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

View Full DocumentRight Arrow Icon
Background image of page 14
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -3 x ( x-4) =-3 x = x-4 = x = x = 4 Now to find the points, you must find the corresponding y-values for these x-values by substituting back into x=0 x=4 Thus, the tangent line to the graph of f is horizontal at the points (0, 0) and (4, 32). f ( x ) = -x 3 + 6 x 2 . f (0) = -3 + 6 ⋅ 2 f (0) = f (4) = -4 3 + 6 ⋅ 4 2 f (4) = 32 Graph for this example Write the equation of the tangent line at a given point on the graph Write the equation of the tangent line to the graph of at the point (-3,9) First find the slope using m = . For this function . At the point (-3,9), f x ( 29 = x 2 , ′ f x ( 29 = 2 x ( 29 ( 29 3 2 3 6 m f ′ =-=-= -( 29 f x ′ Now use m = -6 and the point (-3,9) to write the equation for the tangent line ( 29 ( 29 y x y x y x y x- = -- -- = -+- = --= --9 6 3 9 6 3 9 6 18 6 9 Thus the tangent line to the graph of at the point (-3,9) is the line f x ( 29 = x 2 , y x = --6 9...
View Full Document

This document was uploaded on 04/03/2011.

Page1 / 14

Differentiablilty & Equation of Tangent Line - -3 x ( x-4)...

This preview shows document pages 1 - 14. Sign up to view the full document.

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