Explanation Given Information: The provided function is f ( x ) = x 4 − 160 x 3 + 7200 x 2 − 40 , 000 . Formula Used: To obtain the relative maxima and minima of a function, 1. Find the first derivative of the function. 2. Set the derivative equal to 0 to obtain the critical points. 3. Evaluate f ′ ( x ) at values of x to the left and one to the right of each critical point to develop a sign diagram. (a) If f ′ ( x ) > 0 to the left and f ′ ( x ) < 0 to the right of the critical value, the critical point is a relative maximum point. (b) If f ′ ( x ) < 0 to the left and f ′ ( x ) > 0 to the right of the critical value, the critical point is a relative minimum point. Calculation: Consider the provided function f ( x ) = x 4 − 160 x 3 + 7200 x 2 − 40 , 000 , Use the simple power rule to differentiate, d y d x = 4 x 3 − 480 x 2 − 14400 x = 4 x ( x 2 − 120 x + 3600 ) = 4 x ( x − 60 ) ( x − 60 ) Equate the above derivative to 0, y ′ = d y d x = 4 x ( x − 60 ) ( x − 60 ) = 0 Evaluate the values of x from the equation: 4 x ( x − 60 ) ( x − 60 ) = 0 x = 0 , 60 Hence, the value(s) of x are x = 0 , 60 . Evaluate the values of the original functions with the critical values: Substitute 0 for x in f ( x ) = x 4 − 160 x 3 + 7200 x 2 − 40 , 000 . y = ( 0 ) 4 − 160 ( 0 ) 3 + 7200 ( 0 ) 2 − 40 , 000 = 0 − 0 + 0 − 40 , 000 = − 40 , 000 Hence, ( 0 , − 40000 ) is a critical point. Substitute 0 for x in f ( x ) = x 4 − 160 x 3 + 7200 x 2 − 40 , 000 . y = ( 60 ) 4 − 160 ( 60 ) 3 + 7200 ( 60 ) 2 − 40 , 000 = 12960000 + 34560000 + 25920000 − 40 , 000 = 4280000 Hence, ( 60 , 4280000 ) is a critical point

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ISBN: 8220100546235

Author: Reynolds

Publisher: CENGAGE L

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Chapter 10.1, Problem 39E

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To calculate: The location of critical points and determines viewing window that shows all the features of the graph f(x)=x4−160x3+7200x2−40,000 and, also sketch the complete graph.

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Chapter 10.1, Problem 38E

Chapter 10.1, Problem 40E

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Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CP Ch. 10.1 - Prob. 3CP Ch. 10.1 - Prob. 4CP Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...

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The location of critical points and determines viewing window that shows all the features of the graph f ( x ) = x 4 − 160 x 3 + 7200 x 2 − 40 , 000 and, also sketch the complete graph.

Solution Summary: The author calculates the location of critical points and determines viewing window that shows all the features of the graph.

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To calculate: The location of critical points and determines viewing window that shows all the features of the graph f(x)=x4−160x3+7200x2−40,000 and, also sketch the complete graph.

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