Question: Constant Function TheoremSuppose f(x)is contimuous ona,b and differentiable on(a,b), then Iff'(x)=0onf(x)axbf(x)a,b(a,b)f(x)a,then f(x)is constant onaxb.(5) State the converse of the CFT(assumef(x)is continuous ona,b and differentiable on(a,b)).

Constant Function TheoremSuppose f(x)is contimuous ona,b and differentiable on(a,b), then Iff'(x)=0onf(x)axbf(x)a,b(a,b)f(x)a,then f(x)is constant onaxb.(5) State the converse of the CFT(assumef(x)is continuous ona,b and differentiable on(a,b)). Prove that theconverse is true.(6) Give an example of a discontimuous function that is not constant (show why we need the requirement that f(x)iscontimuous).

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