For number 4, if the derivative is zero, the function is constant - not necessarily zero.
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
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