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\(\text { Let } f(x)=\left\{\begin{array}{cc}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\0 & , x=0\end{array} ; \te…

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\(\text { Let } f(x)=\left\{\begin{array}{cc}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\0 & , x=0\end{array} ; \text { Then at } x=0\right.\)

[JEE Main 2023, 24 Jan (Shift 1)]

a

\(f \text { is continuous but not differentiable }\)

b

\(f \text { is continuous but } f^{\prime} \text { is not continuous }\)

c

\(f \text { and } f^{\prime} \text { both are continuous }\)

d

\(f^{\prime} \text { is continuous but not differentiable }\)

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