Question

g (x) = xf (x) where f (x) = x sin 1/x, x ≠ 0, x = 0, at x = 0 : 

(a) g is differentiable while f is not continuous 

(b) g is differentiable but g ′ is not continuous 

(c) g is differentiable but g ′ is continuous 

(d) both f and g are differentiable

Answer 1

Correct option (c) g is differentiable but g ′ is continuous

Explanation:

Hence g ′ is continuous, and g (x) is differentiable