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Given the following function y = (2x – 2)5, find the value of x where the function takes an optimal point. State the nature of the optimal point. -

Given the following function y = (2x – 2)5, find the value of x where the function takes an optimal point. State the nature of the optimal point. -

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q4

 

Good Afternoon can you please solve question 4 which is equation (2x-2)^5 in the same way has the resolved question 4 with a different equation has been resolved.

 

Thank you

4. Given the following function y = (2x – 2)5, find the value of x where the function takes an optimal point. State the nature of the optimal point. %3D |
Transcribed Image Text:4. Given the following function y = (2x – 2)5, find the value of x where the function takes an optimal point. State the nature of the optimal point. %3D |
4. Given the following function y = (4x – 2)4, find the value of x where the function takes an optimal point. State the nature of the optimal point. - f1 = 4(4x – 2)³(4) = 0; at x = %3D - 1 f11 = 48(4x – 2)²(4) = 0; at x 1 f 111 = 384(4x –- 2)(4) = 0; at x 2 fiv = 6144 > 0 Since we have differentiated an EVEN number of times to find a non- zero derivative, we have either a maximum or minimum. But since the value of the fourth derivative is positive it must be a minimum. See the nth derivative test. - IN || || HIN
Transcribed Image Text:4. Given the following function y = (4x – 2)4, find the value of x where the function takes an optimal point. State the nature of the optimal point. - f1 = 4(4x – 2)³(4) = 0; at x = %3D - 1 f11 = 48(4x – 2)²(4) = 0; at x 1 f 111 = 384(4x –- 2)(4) = 0; at x 2 fiv = 6144 > 0 Since we have differentiated an EVEN number of times to find a non- zero derivative, we have either a maximum or minimum. But since the value of the fourth derivative is positive it must be a minimum. See the nth derivative test. - IN || || HIN
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