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If \(f(x) = \left\{ \begin{array} { l l } { x - 5 } & { x \leq 1 } \\ { 4 x ^ { 2 } - 9 } & { 1 < x < 2 } \\ { 3 x + 4 } & { x \geq 2 } \end{array} \right.\) then \(f' \left( 2 \right) =\) is
(A) \(0\)
(B) \(2\)
(C) \(3\)
(D) \(4\)

Answer

Answer: C
\(f(x=\begin{cases} x-5 \quad \quad ,x\le 1 \\ 4{ x }^{ 2 }-9\quad ,1\lt x<2 \\ 3x+4\quad ,x\ge 2 \end{cases}\)
\(f^1(2)=?\)
Here
\(f(x)=3x+4(x\ge2)\\ \Rightarrow f^1(x)=3\\ \Rightarrow f^1(2)=3\)
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