A) \[a=2,b=3\]
B) \[a=3,b=2\]
C) \[a=-2,b=-3\]
D) \[a=-3,b=-2\]
Correct Answer: A
Solution :
Here, \[f'(x)\,=\left\{ \begin{matrix} 2bx+a & x\ge -1 \\ 2ax, & x<-1 \\ \end{matrix} \right.\] Given, f?(x) is continuous everywhere, \[\Rightarrow \,3a=2b\] Also, \[\,\underset{x\to -{{1}^{+}}}{\mathop{Lim}}\,\,f(x)\,=\,\underset{x\to -{{1}^{-}}}{\mathop{Lim}}\,\,f(x)\] \[\Rightarrow \,b-a+4=a+b\Rightarrow \,2a=4\Rightarrow \,a=2\] Hence, b = 3[from equation 1]You need to login to perform this action.
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