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Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y = x lnx-x+(Ink)x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x-x x lnx-x+ (In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.

Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y = x lnx-x+(Ink)x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x-x x lnx-x+ (In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y=xlnx-x+(Ink) x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x - x x ln x-x+(In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.
Transcribed Image Text:Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y=xlnx-x+(Ink) x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x - x x ln x-x+(In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.
Prove or disprove your conjecture.
Transcribed Image Text:Prove or disprove your conjecture.
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