If f(x) = {(2a - x for -a < x < a), (3x - 2a for x ≥ a) then which one of the following is true? (a) f(x) is not differentiable at x = a

Question

If \(f(x) = \begin{cases} 2a-x & \quad \text{for } -a < x < a \text{}\\ 3x-2a & \quad \text{for } x≥a \text{ } \end{cases}\) then which one of the following is true? 

(a) f(x) is not differentiable at x = a 

(b) f(x) is discontinuous at x = a 

(c) f(x) is continuous for all x in R 

(d) f(x) is differentiable for all x ≥ a

Answer 1

(a) f(x) is not differentiable at x = a

f(x) is not differentiable at x = a