Consider the polynomial f(x) = x 3 −3x 2 +x−3. One root of this polynomial is r = 3. Now consider the polynomial fϵ(x) = (1 + ϵ)x 3 − 3x 2 + x − 3, where ϵ is small.(a) Using the sensitivity formula for rootfinding, predict the shift in the root ∆r from r = 3 as a function of ϵ. What does this tell you about how errors in the coefficient of the cubic term of the input (backward error) are magnified in the output of rootfinding (forward error)