If the functions f and g are defined for all real numbers and f is an anti-derivative of g, which of the following statements is NOT necessarily

correct?

1.If g(x) > 0 for all x, then a is increasing

2.if g(a) = 0 then the graph of a has a horizontal tangent at x = a

3. If f(x) = 0 for all x, then g(x) = 0 for all x

4.if g(x) = 0 for all x, then f(x) = 0 for all x - ANSWER - Why?

5.f is continuous for all x