Explanation Given Information: The function is y = x 2 ln x . Formula Used: Product rule, d d x ( u ⋅ v ) = u ′ ⋅ v + u ⋅ v ′ , where u and v are two separate functions. Derivative of logarithmic function, d d x ( ln x ) = 1 x Power rule of differentiation, d d x ( x n ) = n x n − 1 Chain rule of differentiation, d d x f ( g ( x ) ) = f ′ ( g ( x ) ) ⋅ g ′ ( x ) Calculation: Consider the provided function y = x 2 ln x . First calculate the derivative of the function. Recall the product rule of derivatives, d d x ( u ⋅ v ) = u ′ v + u v ′ Apply the product rule ton given function to get, y ′ = d d x ( x 2 ln x ) = d d x x 2 ⋅ ln ( x ) + x 2 ⋅ d d x ( ln x ) Recall, the chain rule of derivatives. By chain rule, d d x f ( g ( x ) ) = f ′ g ( x ) ⋅ g ′ ( x ) Apply the chain rule to get, y ′ = d d x x 2 ⋅ ln ( x ) + x 2 ⋅ d d x ( ln x ) = d d x x 2 ⋅ ln ( x ) + x 2 ⋅ d d x ( ln x ) ⋅ d d x x Recall, the property of derivative, Properties of derivative, d d x ( ln x ) = 1 x Also, recall the power rule, d d x ( x n ) = n x n − 1 Apply the properties on the given function to get, y ′ = d d x x 2 ⋅ ln ( x ) + x 2 ⋅ d d x ( ln x ) ⋅ d d x x = 2 x 2 − 1 ⋅ ln x + x 2 ⋅ 1 x ⋅ 1 = 2 x ⋅ ln x + x = 2 x ln x + x To find the relative maxima and relative minima put the derivative of the function equal to zero to get the value of x , y &#

11th Edition

ISBN: 8220100546235

Author: Reynolds

Publisher: CENGAGE L

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Chapter 11.1, Problem 40E

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To calculate: The value of relative maxima and relative minima for the function y=x2lnx and sketch the graph using graphing calculator to check.

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Chapter 11.1, Problem 39E

Chapter 11.1, Problem 41E

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Chapter 11 Solutions

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Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The value of relative maxima and relative minima for the function y = x 2 ln x and sketch the graph using graphing calculator to check.

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To calculate: The value of relative maxima and relative minima for the function y=x2lnx and sketch the graph using graphing calculator to check.

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Chapter 11 Solutions