Question

F(x) = x4/5(x − 6)2 find the critical numbers of the function

Answer 1

You can find the critical numbers by finding the derivative of the function and solving for 0.

F(x) = x(4/5)(x-6)(2) = x(8/5)(x-6) = (8/5)(x^2 - 6x)

Taking the derivative:
F'(x) =  (8/5)(2x - 6)
F'(x) = 0 at x = 3, 

critical number = 3