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\(\text { If } f(x)=\left\{\begin{array}{cc}\int_0^x(5+|1-t|) d t, & x>2 \\5 x+1, & x \leq 2\end{array}\right. \text {, …

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\(\text { If } f(x)=\left\{\begin{array}{cc}\int_0^x(5+|1-t|) d t, & x>2 \\5 x+1, & x \leq 2\end{array}\right. \text {, then }\)

[JEE Main 2021, 25 Jul (Shift 2)]

a

\(f(x) \text { is not continuous at } x=2\)

b

\(f^{\prime}(x) \text { is not differentiable at } x=1\)

c

\(f(x) \text { is continuous but not differentiable at } x=2\)

d

\(f(x) \text { is everywhere differentiable }\)

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