Explanation Given information: The provided function is: y = x 2 − 10 ( x − 1 ) 2 3 Calculation: Consider the function: y = x 2 − 10 ( x − 1 ) 2 3 Differentiate above equation with respect to x to get: d y d x = d d x ( x 2 − 10 ( x − 1 ) 2 3 ) = d d x ( x 2 ) + d d x ( − 10 ( x − 1 ) 2 3 ) = 2 x − 20 3 ( x − 1 ) − 1 3 Thus, d y d x = 2 x − 20 3 ( x − 1 ) − 1 3 Draw the graph of f ( x ) by using Ti-83 calculator and the steps are as follows: Step 1: Open Ti-83 calculator. Step 2: Press “Y=” key. Step 3: Press Y 1 = x ^ 2 − 10 ( x − 1 ) ^ 2 / 3 . Step 4: Press “WINDOW” key and set Xmin = − 4 and Xmax = 4 . Step 5: Press “GRAPH” key. The graph of f ( x ) is shown below: Draw the graph of f ′ ( x ) by using Ti-83 calculator and the steps are as follows: Step 1: Open Ti-83 calculator. Step 2: Press “Y=” key. Step 3: Press Y 1 = 2 x − ( 20 ( x − 1 ) ^ − 1 3 ) / 3 . Step 4: Press “WINDOW” key and set Xmin = − 4 and Xmax = 4 . Step 5: Press “GRAPH” key. The graph of f ′ ( x ) is shown below: Since, the stationary points are those points where the graph of f ′ ( x ) cuts the x − axis, thus the use the zoom in feature of the calculator to find the values of x where y = 0 and the steps are as follows: Step 1: Open Ti-83 calculator. Step 2: Press “Y=” key. Step 3: Press 2 x − ( 20 ( x − 1 ) ^ − 1 3 ) / 3 . Step 4: Press “WINDOW” key and set Xmin = − 4 and Xmax = 4

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ISBN: 8220103612005

Author: Costenoble

Publisher: CENGAGE L

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 12.1, Problem 46E

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To calculate: The x− coordinates of the critical points, accurate to two decimal places for the function y=x2−10(x−1)23 with domain (−4,4) and all relative and absolute maxima and minima by using graphing technology.

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Chapter 12.1, Problem 45E

Chapter 12.1, Problem 47E

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Chapter 12 Solutions

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The x − coordinates of the critical points, accurate to two decimal places for the function y = x 2 − 10 ( x − 1 ) 2 3 with domain ( − 4 , 4 ) and all relative and absolute maxima and minima by using graphing technology.

Solution Summary: The author calculates the x- coordinates of the critical points, accurate to two decimal places, by using graphing technology.

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To calculate: The x− coordinates of the critical points, accurate to two decimal places for the function y=x2−10(x−1)23 with domain (−4,4) and all relative and absolute maxima and minima by using graphing technology.

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Chapter 12 Solutions