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A function f is defined on an interval [...

A function f is defined on an interval [a, b]. Which of the following statement(s) is are incorrect? (A) If f(a) and f(b) have opposite signs,then there must be a point `cin(a,b)` such that f(c)=0.

A

if f(a ) and f(b) have opposite sings then there must be a point `c in (a,b) ` such that f(c ) =0

B

if f is continuous on `[a,b] , f(a) lt 0, and f(b)gt 0,` then there must be point ` c in (a,b) ` such that f( c) =0.

C

if f is continuous on [a,b] , and there is point c in (a,b) such that f( c) -0 , then f(a) and f(b) have opposite signs

D

if f has no zeros on [a,b] then f(a) and f(b) have the same sign.

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The correct Answer is:
A, C, D
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