Question

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.

Answer 1

Just because the graph is constant, that does not mean that f = 0.

Answer 2

F(6)=