Lesson07_-_The_Derivative_ws

# Lesson07_-_The_Derivative_ws - f x and give its domain 4...

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Worksheet for Section 2.1–2 The Derivative and Rates of Change The Derivative as a Function V63.0121, Calculus I Spring 2010 1. Let f ( x ) = x 3 . Use the deﬁnition of the derivative to ﬁnd f 0 (2). 2. Let f ( x ) = x . (a) Use the deﬁnition of the derivative to ﬁnd f 0 (4). (b) Find f 0 ( x ) and give its domain. (c) Is f diﬀerentiable at zero? Use a graph to illustrate why or why not. 1

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Here’s a useful fact: for any numbers A and B : A 3 - B 3 = ( A - B )( A 2 + AB + B 2 ) 3. Let f ( x ) = 3 x = x 1 / 3 . Use the deﬁnition of the derivative to ﬁnd

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Unformatted text preview: f ( x ) and give its domain. 4. Repeat with f ( x ) = x 2 / 3 . 2 5. Match the graph of each function in A–D with the graph of this derivative in I–IV. Give reasons for your choices. (A) (B) (C) (D) x y x y x y (I) (II) (III) (IV) x y x y x y x y 3 6. Graphs of f , f , and f 00 are shown below. Which is which? How can you tell? x y 4...
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## This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.

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Lesson07_-_The_Derivative_ws - f x and give its domain 4...

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