f(x)=x ^2 +bx+c , b and c real .Find the minimum of (max|f(x)|)for x∈[−10,10]?

Answer 1

f(x) = x^2 - 100

has maximum value of 0 in [10,10]

For any b,c note equal to (0,-100), the max of f(x) will be nonzero.

So, min(max(|f(x)|)) = 0

Answer 2

50