Find the critical points, domain endpoints, and local extreme values for the fun

Question

Find the critical points, domain endpoints, and local extreme values for the function y = x^2/3(x - 1) From the critical point(s) and domain endpoint(s), what is/are the point(s) corresponding to local maxima? Select necessary, fill in the answer box to complete your choice The point(s) corresponding to the local maxima is/are (0.0). (Type an ordered pair Use integers or decimals for any numbers in the expression Round to the nearest comma to separate answers as needed) There are no points corresponding to local maxima From the critical point(s) and domain endpoint(S) what is/are the point(s) corresponding to local minima? Select necessary, fill in the answer box to complete your choice The point(s) corresponding to the local minima is/are (0 4. - 0 326) (Type an ordered par Use integers or decimals tor any numbers in the expression Round to the nearest, comma to separate answers as needed) There are no points corresponding local minima Question is complete Tap or the red indicators to see incorrect answers All parts showing ________

Explanation / Answer

ans) y = x2/3(x-1)

critical points occur at y' =0

y' = d(x2/3(x-1))/dx = (2/3)x-1/3(x-1) + x2/3

(2/3)x-1/3(x-1) + x2/3 = 0

(2/3)(x-1) + x= 0

2x-2+3x=0

x = 2/5

f(2/5) = (2/5)2/3(2/5-1) = (-3/5)(2/5)2/3 = 0.32

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