Let \(f:[-1,1] \rightarrow R\) be defined \(a\) s \(f(x)=a x^2+b x+c\) for all \(x \in[-1,1]\), where \(a, b, c \in \mat…

Let \(f:[-1,1] \rightarrow R\) be defined \(a\) s \(f(x)=a x^2+b x+c\) for all \(x \in[-1,1]\), where \(a, b, c \in \mathrm{R}\) such that \(f(-1)=2, f^{\prime}(-1)\) \(=1\) and for \(x \in(-1,1)\) the maximum value of \(f^{\prime \prime}(x)\) is \(\frac{1}{2}\). If \(f(x) \leq \alpha, x \in[-1,1]\), then the least value of \(\alpha\) is equal to........

[JEE Main 2021, 17 Mar (Shift 2)]