Today as our professor went over second and third derivatives, it all finally clicked. Especially now that I know that calculus was a means to further Isaac Newton’s study in the area of Physics, I realize why derivatives help with that.

Here’s the analogy our professor gave us:

Imagine you’re driving down the highway. If the original function gives the position of the car, the first derivative gives the car’s velocity as it moves down the highway, the second derivative gives the acceleration of the car, and the third derivative is the jerk that occurs as it accelerates. Pretty interesting. So I made a visual diagram to sort of drive it home. Pun TOTALLY intended.

Note here that I’m driving a very awesome convertible. The velocity is demonstrated by my hair blowing in the wind, the acceleration is more imagined here, just imagine me with my foot pressing on the gas… “the jerk” has to do with that jerk you feel as you accelerate, and I like to think the original function here would be the dot on the GPS. If you can’t see it, just click on the photo and it will enlarge for you.

The biggest issue I’m having now is remembering all the rules for e^x and natural logs. So I’m going to be doing some more research into that and hopefully posting some very important rules asap.