Consider the function f(x)=2x3-3x.We are interested in a root xoff suchthat x>0.Find a bracketing interval I containing x.Check that xis a unique, simple root offin I.Check that f,f' and f'' are continuous over I, and use Newton's methodto design a recurrence xn+1=g(xn) which will converge tox.Check that g(x)is continuous over I.Isg(x) a contraction over I ?If not, show that there exists a new intervalJ=[a,b] such that g(x)is a contraction over Ja and bto prove this.