Find Constants $a \text { and } b$ So That $f ( x ) = \left\{ \begin{array} { l l } a x + b & \text { if } x < 1 \\b x ^ { 2 } + 1 & \text { if } x \geq 1\end{array} \right.$

Multiple Choice

Find constants $a \text { and } b$ so that $f ( x ) = \left\{ \begin{array} { l l } a x + b & \text { if } x < 1 \\b x ^ { 2 } + 1 & \text { if } x \geq 1\end{array} \right.$ , is continuous and differentiable everywhere?

A) $a = 2 , b = 1$
B) $a = 1 , b = 1$
C) $a = 1 , b = \frac { - 1 } { 2 }$
D) $a = 1 , b = \frac { 1 } { 2 }$