Copy_of_3.1notestouse

Copy_of_3.1notestouse - y = 3 Relationship between the...

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Calculus Section 2.1 Page1 3.1 Derivative of a Function Definition of the Derivative Example 1 Applying the Definition Differentiate (that is, find the derivative of) f x ( ) = x 3

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Calculus Section 2.1 Page 2 Alternate Definition of the Derivative at a Point Example 2 Applying the Alternate Definition Differentiate f x ( ) = x using the alternate definition. Solve Numerically (make a table) Notation Example 3 Recognizing a given limit as a derivative Given f x ( ) , determine f x ( ) . a) lim h 0 x + h ( ) 2 - x 2 h b) lim h 0 x + h 3 - x 3 h
Calculus Section 2.1 Page3 c) lim h 0 tan x + h ( ) - tan x h d) lim h 0 x + h x + h ( ) 2 + 1 - x x 2 + 1 h e) lim h 0 e x + h - e x h f) lim h 0 1 h 1 x + h - 1 x Example 4 Expressing the derivative as a limit Express the derivative of each of the following functions as a limit. a) y = cos x b) y = 3 x c)

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Unformatted text preview: y = 3 Relationship between the graphs of f and ′ f Example 5 Graphing ′ f from f Calculus Section 2.1 Page 4 Example 6 Graphing f from ′ f Calculus Section 2.1 Page5 One-Sided Derivatives The Right-hand derivative at a The Left-hand derivative at a Example 7 One-Sided Derivatives Can Differ at a Point Show that the following funciton has left-hand and right-hand derivatives at x = 0 , but no derivative there. f x ( ) = x 2 , x ≤ 2 x , x > Calculus Section 2.1 Page 6 Assignment II-1 Page 101 – 102 #1 – 10 all, 12 (use notes for derivative of y = x 3 ), 13, 16, 17, 18, 22, Recognizing the Limit as a Derivative Sheet...
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Copy_of_3.1notestouse - y = 3 Relationship between the...

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