Explanation Given: The function f ( x ) = { x 2 − 3 , i f x < 3 x + 2 , i f x ≥ 3 x = 3 Concept used: The left derivative and right derivative of a function f at a point x = c are , equal f − ' ( c ) = lim h → 0 − f ( c − h ) − f ( c ) − h f + ' ( c ) = lim h → 0 + f ( c + h ) − f ( c ) h Calculation: The function y = f ( x ) = { x 2 − 3 , i f x < 3 x + 2 , i f x ≥ 3 x = 3 ............. ( 1 ) The left derivative and right derivative of a function f at a point x = c are , equal f − ' ( c ) = lim h → 0 − f ( c − h ) − f ( c ) − h f + ' ( c ) = lim h → 0 + f ( c + h ) − f ( c ) h The right derivative of f at x = 3 Here, h > 0 then 3 + h > 3 use the second part of the piecewise −defined function f f + ' ( 3 ) = lim h → 0 + f ( 3 + h ) − f ( 3 ) h

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 2.2, Problem 74S

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The function f(x)={x2−3 ,if x<3x+2, if x≥3 x=3 is differential or not at the value of x

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Chapter 2.2, Problem 73S

Chapter 2.2, Problem 75S

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The function f ( x ) = { x 2 − 3 , i f x < 3 x + 2 , i f x ≥ 3 x = 3 is differential or not at the value of x

Solution Summary: The author explains that the left and right derivatives of a function f at x=c are equal, but not differential.

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The function f(x)={x2−3 ,if x<3x+2, if x≥3 x=3 is differential or not at the value of x

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Chapter 2 Solutions

The function f ( x ) = { x 2 − 3 , i f x &lt; 3 x + 2 , i f x ≥ 3 x = 3 is differential or not at the value of x

Solution Summary: The author explains that the left and right derivatives of a function f at x=c are equal, but not differential.

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To find: The function f(x)={x2−3 ,if x<3x+2, if x≥3 x=3 is differential or not at the value of x

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Chapter 2 Solutions

The function f ( x ) = { x 2 − 3 , i f x < 3 x + 2 , i f x ≥ 3 x = 3 is differential or not at the value of x

To find:

The function f(x)={x2−3 ,if x<3x+2, if x≥3 x=3 is differential or not at the value of x