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Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x4 − 4x3 + 16x − 16   Test the values of y' and y'' as shown in the table to find the relative extrema and points of inflection.   Identify any asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)

Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x4 − 4x3 + 16x − 16   Test the values of y' and y'' as shown in the table to find the relative extrema and points of inflection.   Identify any asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 64PFA
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Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)
y = x4 − 4x3 + 16x − 16
 
Test the values of y' and y'' as shown in the table to find the relative extrema and points of inflection.
 
Identify any asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)
 
Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x - 4x + 16x - 16 STEP 1: Set the factors of the function of y equal to zero and solve for the x-intercepts. y = x* - 4x + 16x - 16 = (x + 2)(x - 2)3 smaller x-value (x, y) = -2,0 larger x-value (х, у) - 2,0 To find the y-intercept, substitute x = 0 in the original function and solve for y. (x, v) = (0, – 16 STEP 2: Set the factors of the first derivative of y equal to zero and solve for the critical numbers. (Enter your answers as a comma-separated list.) y' = 4x - 12x+ 16 = 4(x + 1)(x - 2) x = -1,2 STEP 3: Set the factors of the second derivative of y equal to zero and solve. (Enter your answers as a comma-separated list.) y" - 12x - 24x = 12x(x - 2) x = 0,2 STEP 4: Test the values of y' and y" as shown in the table to find the relative extrema and points of inflection. Interval -* <x< -1 -1 <x< 0 0 <x < 2 2 <x< Sign of y' y'<0 y'>0 y'> 0 y'> 0 Sign of y" y">0 y" >0 y" <0 y"> 0 relative minimum (x, y) - points of inflection smaller x-value (x, y) = larger x-value (x, y) = STEP 5: Identify any asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.) horizontal asymptote vertical asymptote
Transcribed Image Text:Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x - 4x + 16x - 16 STEP 1: Set the factors of the function of y equal to zero and solve for the x-intercepts. y = x* - 4x + 16x - 16 = (x + 2)(x - 2)3 smaller x-value (x, y) = -2,0 larger x-value (х, у) - 2,0 To find the y-intercept, substitute x = 0 in the original function and solve for y. (x, v) = (0, – 16 STEP 2: Set the factors of the first derivative of y equal to zero and solve for the critical numbers. (Enter your answers as a comma-separated list.) y' = 4x - 12x+ 16 = 4(x + 1)(x - 2) x = -1,2 STEP 3: Set the factors of the second derivative of y equal to zero and solve. (Enter your answers as a comma-separated list.) y" - 12x - 24x = 12x(x - 2) x = 0,2 STEP 4: Test the values of y' and y" as shown in the table to find the relative extrema and points of inflection. Interval -* <x< -1 -1 <x< 0 0 <x < 2 2 <x< Sign of y' y'<0 y'>0 y'> 0 y'> 0 Sign of y" y">0 y" >0 y" <0 y"> 0 relative minimum (x, y) - points of inflection smaller x-value (x, y) = larger x-value (x, y) = STEP 5: Identify any asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.) horizontal asymptote vertical asymptote
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