Graphing Functions and Their Derivatives

1. When a first derivative is positive, the original function is increasing.
2. When a first derivative is negative, the original function is decreasing.
   1. The derivative does not tell us if the function is positive or negative, only if increasing or decreasing.
3. When a second derivative is positive, the original function is concave up.
4. When a second derivative is negative, the original function is concave down.
5. When a first derivative hits zero from below the axis, the original function is at a(n) local minimum.
6. When a second derivative is zero, the original function is at a(n) inflection point.