Differentiability of Piecewise Functions at a Point
Let f and g be functions such that f(x) = x²sin(1/x) and g(x) = xsin(1/x) for x ≠ 0, and f(0) = g(0) = 0. Which of the following statements is true?
A
f is differentiable at x = 0 but g is not
B
g is differentiable at x = 0 but f is not
C
Both f and g are differentiable at x = 0
D
Neither f nor g is differentiable at x = 0
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