Okay, I'll try a little better this time.
For a function, its derivative equals its slope.
In this graph, you see the function x^3. Roughly. Yes, it's a paint job. You can see that as x approaches zero from both sides, the slope gets smaller until it actually equals zero. But the whole time, the slope is positive (except zero, cuz zero isn't positive or negative).
This is the graph of the derivative, x^2. You can see that it is positive the whole time except when x=0. There, the y value becomes zero.
Hope this helped...