# Thread: Domain of Derivative and Integral

1. ## Domain of Derivative and Integral

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

2. ## Re: Domain of Derivative and Integral

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

- Hollywood

3. ## Re: Domain of Derivative and Integral

Originally Posted by hollywood
For number 4, if the derivative is zero, the function is constant - not necessarily zero.

- Hollywood
Thanks.

4. ## Re: Domain of Derivative and Integral

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

5. ## Re: Domain of Derivative and Integral

I assume he means 1. If g(x) > 0 for all x then f is increasing.

- Hollywood