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Given that a function f is continuous on [a,b] that is fC[a,b] and p(a,b). a. Since, f is continuous on [a,b] it implies that it is also continuous at p(a,b) By using the definition of continuity of a function for every real number >0 there exists a real number >0 depending on such that f(x)f(p)0,f(p)0 then 0.9f(p)>0 but, 0.9f(p)0(1) If f(p)0 with f(x)=0 for all x[p,p+]With[p,p+][a,b] b. Since, f is continuous on [a,b] it implies that it is also continuous at p(a,b) By using the definition of continuity of a function for every real number >0 there exists a real number >0 depending on such that f(x)f(p)0 set =k and restrict so that a

0 there exists >0 with f(x)0 there exists a real number >0 depending on such that f(x)f(p)0,f(p)0 then 0.9f(p)>0 but, 0.9f(p)0(1) If f(p)0 with f(x)=0 for all x[p,p+]With[p,p+][a,b] b. Since, f is continuous on [a,b] it implies that it is also continuous at p(a,b) By using the definition of continuity of a function for every real number >0 there exists a real number >0 depending on such that f(x)f(p)0 set =k and restrict so that a

0 there exists >0 with f(x)