How Does Sketching a Derivative from the Graph of a Function Work?

Imagine you're sliding down a wiggly slide, how fast you're going depends on how steep the slide is at that moment. That's what sketching a derivative from the graph of a function is like: it’s showing you how steep things are as you move along.

Think of the original graph as the wiggly slide itself, it shows your height above the ground as you go down. Now, if you draw a new picture that shows how fast you're sliding at each point, that’s like drawing the derivative of the function.

To do this, imagine stopping at different spots on the slide and checking how steep it is there, if the slide is going up sharply, the derivative is high; if it's flat, the derivative is low or even zero. You’re basically taking a snapshot of the slope everywhere on the slide and drawing that as a new graph.

You can do this by looking at each part of the original graph, is it going up, down, or staying flat? Then you draw little lines showing how steep it was. If you connect all those little lines, you get the derivative graph, a picture of speed from a picture of height! Imagine you're sliding down a wiggly slide, how fast you're going depends on how steep the slide is at that moment. That's what sketching a derivative from the graph of a function is like: it’s showing you how steep things are as you move along.

Think of the original graph as the wiggly slide itself, it shows your height above the ground as you go down. Now, if you draw a new picture that shows how fast you're sliding at each point, that’s like drawing the derivative of the function.

To do this, imagine stopping at different spots on the slide and checking how steep it is there, if the slide is going up sharply, the derivative is high; if it's flat, the derivative is low or even zero. You’re basically taking a snapshot of the slope everywhere on the slide and drawing that as a new graph.

You can do this by looking at each part of the original graph, is it going up, down, or staying flat? Then you draw little lines showing how steep it was. If you connect all those little lines, you get the derivative graph, a picture of speed from a picture of height!