I recall a similar exercise on my AP Calc exam from years ago. Instead of sketching the derivative based on the graph of a function, we had to sketch the funct

I recall a similar exercise on my AP Calc exam from years ago. Instead of sketching the derivative based on the graph of a function, we had to sketch the function based on a table of data which described the function as well as its first and second derivatives in terms of value, existence, and sign at various points and intervals.