
Yefim S. answered 01/16/20
Math Tutor with Experience
Problem only point x = 2. To be continious at x = 2 limf(x) = f(2) = 22 = 4, lim f(x) = 2m + b = 4, x tends to 2.
Now f'(2) = 2x = 2·2 = 4. On the other hend f'(x) = m, f'(2) = m = 4, 2m + b = 4, 2·4 + b = 4, b = -4.
f(x) = x2 for x ≤ 2 and f(x) = 4x - 4 for x > 2 continious and differentiable at x = 2 and because differentiable for all x.