Are the graphs I sketched of the derivative of a function and the function correct? I know that when the function is increasing, the derivative is positive. What I am confused about for the first one is that when I am sketching the derivative, I don't know what direction it goes (even though i know it is positive). What I am thinking is that where the graph has a min or max, then the derivative must have an x-intercept there. That is how I came up with my graph for the first two questions. 

For the third question, I tried doing the opposite. So the derivative is positive thus the function is increasing and vice versa. Where the derivative has an x-intercept, the function has a min or max but the question is still a little confusing to me.
I think it would be helpful for you to discretize your graph along X axis and calculate the derivative using some finite differences formula.
I think it would be helpful for you to discretize your graph along X axis and calculate the derivative using some finite differences formula.