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: 9780100546233

Author: Reynolds

Publisher: YUZU

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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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(a) Test the hypothesis. Consider the hypothesis test Ho = : against H₁o < 02. Suppose that the sample sizes aren₁ = 7 and n₂ = 13 and that $² = 22.4 and $22 = 28.2. Use α = 0.05. Ho is not ✓ rejected. 9-9 IV (b) Find a 95% confidence interval on of 102. Round your answer to two decimal places (e.g. 98.76).

Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 = 0. What level of type II error would you recommend here? Round your answer to four decimal places (e.g. 98.7654). Use a = 0.05. β = i What sample size would be required? Assume the sample sizes are to be equal.…

= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.

Chapter 11 Solutions

EBK MATHEMATICAL APPLICATIONS FOR THE M

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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