Continuity and Differentiability of a Piecewise Function
Let the function f be defined by f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x}\right) & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}. Which of the following statements is true?
A
f is neither continuous nor differentiable at x=0
B
f is both continuous and differentiable at x=0
C
f is differentiable at x=0 but not continuous at x=0
D
f is continuous at x=0 but not differentiable at x=0
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