Riley, I've been thinking about the derivative. {{CMD_7}} It's all about change. It's some ``change-detector'' tool for math. {{CMD_8}} I know! What's crazy is that you can use it as a tool for sniffing out dirt on functions. {{CMD_9}} First {{MATH_10}} tells us increasing or decreasing. {{CMD_11}} Then {{MATH_12}} tells us concavity. {{CMD_13}} From just that we know all local maxes and mins. {{CMD_14}} And if we use limits, we can find any asymptotes! {{CMD_15}} You know, I'd like to make up a procedure based on all these facts, that would tell me what the graph of any function would look like. {{CMD_16}} Me too! Let's get to work! {{CMD_17}}