Find all critical values for the function

f(x)=x^1/11(x-1)^2
I used the product rule and I got 2 critical points (0,0) and (1,0). Help, please.

f(x) = x^(1/11) (x - 1)^2 = x^(1/11) (x^2 - 2x + 1) = x^(23/11) - 2x^(12/11) + x^(1/11)

f'(x) = (23/11)x^(12/11) - 2(12/11)x^(1/11) + (1/11)x^(-10/11) = 0
x^(-10/11) [(23/11)x^2 - (24/11)x + (1/11)] = 0
x ≠ 0 (1/11) (23x^2 - 24x + 1) = 0
(23x - 1)(x - 1) = 0
x = 1/23 or x = 1

(1, 0) is a critical point; (1/23, 0.688) is also a critical point.

Don't understand your syntax. Do you mean

(x^1)/11(x-1)^2 ... so this is x divided by 11(x-1)^2 ... or

x^(1/11)(x-1)^2 ... which is x to the 1/11 times (x-1)^2 ??