homwork help please

Question

Consider the function .

For this function there are two important open intervals:  and  where  is a critical number. Find    

Answer 1

c is a critical value of f(x) = f'(c) = 0 or if f is not differentiable at c.

f(x) = 4(x-4)^(2/3)

f'(x) = (8/3)(x-4)^(-1/3)

f'(x) = 8/[3(x-4)^(1/3)]

f'(x) is not differentiable at x = 4 (division by zero)

Thus the value of A is 4.