If the functions f and g are defined for all real numbers and f is an antiderative of g, which of the following statements is NOT necessarily true?
(A)If g(x)>0 for all x, then f is increasing
(B)If g(a)=0, then f(x) has a horizontal tangent at x=a
(C)If f(x)=0 for all x, then g(x)=0 for all x
(D)If g(x)=0 for all x, then f(x)=0 for all x
(E)f is continuous for all x
I know the answer is D, but I need an explanation as to why, please and thanks.
2 answers
Just because the graph is constant, that does not mean that f = 0.
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