Let `f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1` Then, `f(x)` is derivable at `x=1` , if `a=2` (b) `b=1` (c) `a=0` (d) `a=1//2`

Explanation

To determine the value of \( a \) for which the function

\[
f(x) =
\begin{cases}
a x^2 + 1 & \text{if } x > 1 \\
\frac{x + 1}{2} & \text{if } x \leq 1
\end{cases}
...