Riley, I might be a calculus genius. {{CMD_7}} Yeah? Explain this one to me. {{CMD_8}} Let me first ask you a question. Say you have a function, like {{MATH_9}}, and you want to know {{MATH_10}}. Do you plug in the number {{MATH_11}} before or after you find the derivative? {{CMD_12}} Hmmmm. Well, my next step is usually {{MATH_13}} So I guess before. {{CMD_14}} Aha! I think you're wasting time. You see I write {{MATH_15}} and it means that I can look at the derivative of my function at {{CMD_16}}any{{CMD_17}} point. So, I plug in the {{MATH_18}} {{{CMD_19}} after} I've found the derivative. {{CMD_20}} That does seem like a pretty genius move. But doesn't working with {{MATH_21}}, instead of numbers, make all of this more difficult? {{CMD_22}} Not at all. Let's do the problems both ways, at the same time: {{CMD_23}} {{ENV_24}} {{CMD_25}} {{CMD_26}} Whoa. So now the derivative is a function. Wait, what's its domain? Its range? {{CMD_27}}