Consider the polynomial f(x) \equal{} ax^2 \plus{} bx \plus{} c, with degree less than or equal to 2.
When f varies with subject to the constrain f(0) \equal{} 0,\ f(2) \equal{} 2, find the minimum value of S\equal{}\int_0^2 |f'(x)|\ dx. calculusintegrationalgebrapolynomialcalculus computations