How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.
When f(x) is increasing, f ' (x) will be positive
When f(x) is decreasing, f ' (x) will be negative
When f(x) is concave down, f '' (x) will be negative
When f(x) is concave up, f '' (x) will be positive
When f(x) changed from increasing to decreasing (or vice versa) f ' (x) = 0
When f(x) changes in concavity, f '' (x)= 0
If it helps you, graph all three on the same graph and look at what changes.