Let f:[−1,1]→R be defined as f(x)=ax2+bx+c for all x∈[−1,1], where a,b,c∈R such that f(−1)=2,f′(−1)=1 and for x∈(−1,1) the maximum value of f′′(x) is 12. If f(x)≤α,x∈[−1,1], then the least value of α is equal to

Let f:[−1,1]→R be defined as f(x)=ax2+bx+c for all x∈[−1,1], w

1.	Let f:[−1,1]→R be defined as f(x)=ax2+bx+c for all x∈[−1,1], where a,b,c∈R such that f(−1)=2,f′(−1)=1 and for x∈(−1,1) the maximum value of f′′(x) is 12. If f(x)≤α,x∈[−1,1], then the least value of α is equal to
Answer» Let $f : [- 1, 1] \to R$ be defined as $f (x) = a x^{2} + b x + c$ for all $x \in [- 1, 1],$ where $a, b, c \in R$ such that $f (- 1) = 2, f^{'} (- 1) = 1$ and for $x \in (- 1, 1)$ the maximum value of $f^{''} (x)$ is $\frac{1}{2} .$ If $f (x) \leq α, x \in [- 1, 1],$ then the least value of $α$ is equal to