Q.The function $f(x) = \begin{cases} x^2 & x < 0 \ x^2 + 1 & x \ge 0 \end{cases}$ is

continuous and differentiable everywhere

continuous everywhere but not differentiable at

x=0

discontinuous at

x=0

differentiable everywhere but not continuous

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)={x2x<0 x2+1x≥0f(x) = \begin{cases} x^2 & x < 0 \ x^2 + 1 & x \ge 0 \end{cases}f(x)={x2​x<0 x2+1​x≥0​ is