(a)(15 marks) Let f(x)be a function defined onan open interval containing a,b and f(x) havesecond derivative at every xin[a,b].Iff'(a)=f'(b)=0, then prove that there exists cin(a,b)such that|f''(c)|4(b-a)2|f(b)-f(a)|(b)(10 marks) Define f:RRas follows:f(x)={e-1x2,ifx00,ifx=0Prove that for any ninN,f(n)(0)=0, which implies that any Taylor polynomials off about 0isa zero polynomial.