30 20 2. ... .. O WebAssign %3D STEP 4: Test the values of y' and y" as shown in the table to find the relative extrema and points of inflection. 7 > x > 0 co > X > Interval 0 > x > T- - > X > 0- 0 < , / 0 < , ^ Sign of y' 0 < , ^ 0 > , ^ 0> „^ 0 < „^ 11 Sign of y " 0< , ^ 0 < ,^ %3D relative minimum = (A 'x) smaller x-value (x, y) = points of inflection larger x-value (x, y) %3D 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 STEP 6: Sketch the graph of the function. 30 07 ot X TT -2 -2 4. -4 NOV 3 27 étvJ MacBook Pro esc $ % i 6 * 00 CO WebAssign Your last submission is used for your score. 5. DETAILS LARAPCALC10 3.7.010.SBS, 0/2 Submissions Used 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 DN y = x* – 4x3 + 16x – 16 %3D STEP 1: Set the factors of the function of y equal to zero and solve for the x-intercepts. y = xª – 4x3 + 16x – 16 %3D = (x + 2)(x – 2)3 %D smaller x-value (A 'x) larger x-value (x, y) To find the y-intercept, substitute x = 0 in the original function and solve for y. (x, y) = 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' = 4x3 - 12x² + 16 = 4(x + 1)(x – 2)2 = X 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" = 12x2 – 24x = 12x(x - 2) = X STEP 4: Test the values of y' and y" as shown in the table to find the relative extrema and points of inflection. NOV 3 27 étv 占S MacBook Pro esc # $ ) 4. ... tab M caps lock S K H

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