Find the functions Derivative and find the x-coordinates of the critical points

Question

Find all relative and absolute maxima and minima. (Order your answers from smallest to largest x. Round your answers to two decimal places.)

y = 4x² − 40(x − 1)^2/3 with domain (−4, 4)

y has___ (x, y) =

Answer 1

0= y' = 8x - (80/3)(x-1)^(-1/3)

multiplies by (x-1)^(1/3):

8x(x-1)^(1/3) - 80/3 = 0

divides by 10:

x(x-1)^(1/3) - 10/3 = 0

examining the graph of this derivative...

x = -2.25 and x = 2.761

(-2.25, -67.514) and (2.761,-27.839)