Explanation Given information:- The given derivative of y = 12 x 2 + 2 x + 4 − x 2 . Calculations:- The given derivative of y = 12 x 2 + 2 x + 4 − x 2 . To find the transition point, we will take the first and second derivative of the given equation as shown below: y = 12 x 2 + 2 x + 4 − x 2 [The given derivative of the equation] y ' = d d x [ 12 x 2 + 2 x + 4 − x 2 ] [Differentiate with respect to x ] y ' = 12 ⋅ d d x [ x 2 + 2 x + 4 ] − d d x [ x 2 ] [Apply power rule [ u ( x ) n ] ' = n ⋅ u ( x ) n − 1 ] y ' = 12 ⋅ 1 2 ( x 2 + 2 x + 4 ) 1 2 − 1 ⋅ d d x [ x 2 + 2 x + 4 ] − 2 x y ' = 6 [ d d x [ x 2 ] + 2 ⋅ d d x [ x ] + d d x [ 4 ] ] x 2 + 2 x + 4 − 2 x [ ∴ , d d x [ x 2 ] = 2 x , d d x [ x ] = 1 ] y ' = 6 ( 2 x + 2 ) x 2 + 2 x + 4 − 2 x Find the second derivative by using first derivative are as shown below: y ' = 6 ( 2 x + 2 ) x 2 + 2 x + 4 − 2 x [Find the second derivative] y ' ' = d d x [ 6 ( 2 x + 2 ) x 2 + 2 x + 4 − 2 x ] [Apply the quotient rule [ u ( x ) v ( x ) ] ' = u ' ( x ) ⋅ v ( x ) − u ( x ) ⋅ v ' ( x ) v ( x ) 2 ] y ' ' = 6 ⋅ d d x [ 2 x + 2 ] ⋅ x 2 + 2 x + 4 − ( 2 x + 2 ) ⋅ d d x [ x 2 + 2 x + 4 ] ( x 2 + 2 x + 4 ) 2 − 2 ⋅ 1 y ' ' = 6 ( ( 2 ⋅ d d x [ x ] + d d x [ 2 ] ) x 2 + 2 x + 4 − 1 2 ( x 2 + 2 x + 4 ) 1 2 − 1 ⋅ d d x [ x 2 + 2 x + 4 ] ⋅ ( 2 x + 2 ) ) x 2 + 2 x + 4 − 2 Again applying the quotient rule [ u ( x ) v ( x ) ] ' = u ' ( x ) ⋅ v ( x ) − u ( x ) ⋅ v ' ( x ) v ( x ) 2 ] to simplify y ' ' = 6 ( ( 2 ⋅ d d x [ x ] + d d x [ 2 ] ) x 2 + 2 x + 4 − 1 2 ( x 2 + 2 x + 4 ) 1 2 − 1 ⋅ d d x [ x 2 + 2 x + 4 ] ⋅ ( 2 x + 2 ) ) x 2 + 2 x + 4 − 2 <

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 4.5, Problem 40E

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The solution of the graph of the equation and indicate all the transition points.

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Chapter 4.5, Problem 39E

Chapter 4.5, Problem 41E

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sketch the graph of the function, indicating all transition points. If necessary, use a graphingutility or computer algebra system to locate the transition points numerically. y = x2 − 10 ln(x2 + 1)

In Exercises 49–52, find an equation for and sketch the graph of the level curve of the function ƒ(x, y) that passes through the given point.

Chapter 4 Solutions

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Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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The solution of the graph of the equation and indicate all the transition points.

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The solution of the graph of the equation and indicate all the transition points.

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Chapter 4 Solutions