Find the critical numbers of the function?

Question

f(x)= x^4/5(x-4)^2

Answer 1

Critical numbers are points where the slope of a function is 0.
f(x) = x^4/5(x - 4)^2 =
f(x) = (1/5)x^4(x - 4)^-2
f'(x) = -2(1/5)x^4(x - 4)^-3 + 4(1/5)x^3(x - 4)^-2 = 0
-2(1/5)(x^4/(x - 4)^3 - 2x^3(x - 4)/(x - 4)^3)= 0
(x^4 - 2x^3(x - 4) = 0
x^3(x - 2x + 8) = 0
x^3(x - 8) = 0
x = 0,8

Answer 2

critical numbers are where f(x) is not defined .. this happens when denominator becomes 0

so, 5(x-4)^2 = 0
u get x = 4

so critical number is 4