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Therefore by the Second Derivative Test, give the following points. (If an answer does not exist, enter DNE.) relative maximum relative minimum inflection point (x, y) = ( (x, y) = ( (x, y) = ( )

Therefore by the Second Derivative Test, give the following points. (If an answer does not exist, enter DNE.) relative maximum relative minimum inflection point (x, y) = ( (x, y) = ( (x, y) = ( )

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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Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. x² - 10x + 65 X-8 y = Step 1 Begin by finding the intercepts. (If an answer does not exist, enter DNE.) To find the y-intercept, substitute x = 0 and solve for y. The y-intercept is 65 8 To find the x-intercept, substitute y = 0 and solve for x. (x, y) = (0, The x-intercept is (x, y) = (DNE y' = Step 2 Next, differentiate the given function y = x² − 10x + 65 and write as a single fraction completely factored. X-8 (2x - 10)(x − 8) 2 65 8 (x - - 8)¹ y" = (x - 1)(x - 15) 2 (x - The derivative y'= 0 when x = 98 (x − 8)³ Substituting x = 15 into y", we see that y" relative maximum (x, y) relative minimum inflection point Step 3 To determine maximums and minimums by the Second Derivative Test, we differentiate y' with respect to x. Substituting x = 1 into y", we see that y" There is no value of x for which y" is zero. (x, y) (x, y) 0, = DNE 15,1 98 = = x² - 10x + 65 (x - 8) Step 4 Therefore by the Second Derivative Test, give the following points. (If an answer does not exist, enter DNE.) ( |). ( 1, 15 > 0. (entered as a comma-separated list). 0.
Transcribed Image Text:Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. x² - 10x + 65 X-8 y = Step 1 Begin by finding the intercepts. (If an answer does not exist, enter DNE.) To find the y-intercept, substitute x = 0 and solve for y. The y-intercept is 65 8 To find the x-intercept, substitute y = 0 and solve for x. (x, y) = (0, The x-intercept is (x, y) = (DNE y' = Step 2 Next, differentiate the given function y = x² − 10x + 65 and write as a single fraction completely factored. X-8 (2x - 10)(x − 8) 2 65 8 (x - - 8)¹ y" = (x - 1)(x - 15) 2 (x - The derivative y'= 0 when x = 98 (x − 8)³ Substituting x = 15 into y", we see that y" relative maximum (x, y) relative minimum inflection point Step 3 To determine maximums and minimums by the Second Derivative Test, we differentiate y' with respect to x. Substituting x = 1 into y", we see that y" There is no value of x for which y" is zero. (x, y) (x, y) 0, = DNE 15,1 98 = = x² - 10x + 65 (x - 8) Step 4 Therefore by the Second Derivative Test, give the following points. (If an answer does not exist, enter DNE.) ( |). ( 1, 15 > 0. (entered as a comma-separated list). 0.
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