Q.The function $f(x) = \begin{cases} x^{3/2}\sin(1/x) & x>0 \ 0 & x\le 0 \end{cases}$ is

differentiable at

x=0

not differentiable at

x=0

not continuous at

x=0

differentiable everywhere

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.The function f(x)={x3/2sin⁡(1/x)x>0 0x≤0f(x) = \begin{cases} x^{3/2}\sin(1/x) & x>0 \ 0 & x\le 0 \end{cases}f(x)={x3/2sin(1/x)​x>0 0​x≤0​ is