Let \( f(x)=\left[\begin{array}{l}x^{2}+a ; 0 \leq x1 \\ 2 x+b ; 1 ...

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Let \( f(x)=\left[\begin{array}{l}x^{2}+a ; 0 \leq x1 \\ 2 x+b ; 1 \leq x \leq 2\end{array}\right. \) and \( g(x)=\left[\begin{array}{c}3 x+b ; 0 \leq x1 \\ x^{3} ; 1 \leq x \leq 2\end{array}\right. \)
\( \mathrm{P} \)
W If derivative of \( f(x) \) w.r.t. \( g(x) \) at \( x=1 \) exists and is equal to \( \lambda \), then which of the following is/are correct ?
(a) \( a+b=-3 \)
(b) \( a-b=1 \)
(c) \( \frac{a b}{\lambda}=3 \)
(d) \( \frac{-b}{\lambda}=3 \)
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