f(x) = (x − 2)^2/5

Question

^ 2/5 exponent

Describe the x-values at which f is differentiable. (Enter your answer using interval notation.)

Answer 1

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

f'(x) = (2/5)(x-2)^-3/5 = (2/5) / (x-2)^3/5

f'(x) is undefined when x = 2. So, f is differentiable for all x except for x = 2.