When you are asked to analyze a function in calculus, be sure to distinguish between positive/negative, increasing/decreasing, and concave up/concave down. These are three different concepts!
Here’s the same function, shown three times.
- The value of the function determines whether it is positive or negative:
- The value of the first derivative determines whether it is increasing or decreasing:
- The value of the second derivative determines whether it is concave up or concave down:
