Domain of Derivative and Integral

Oct 2012
1,314
21
USA
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
 
Last edited:
Mar 2010
1,055
290
For number 4, if the derivative is zero, the function is constant - not necessarily zero.

- Hollywood
 
Jul 2012
863
232
INDIA
1. What is a. If g(x) > 0 for all x then g(x) is increasing.
 
Mar 2010
1,055
290
I assume he means 1. If g(x) > 0 for all x then f is increasing.

- Hollywood