# Thread: How do I Graph the First and Second Derivative of a Function with no Equation?

1. ## How do I Graph the First and Second Derivative of a Function with no Equation?

I've been given 2 graphs that represent s(t), and I need to find v(t) and a(t) of each graph, the first and second derivatives of s(t). Does anyone know how to do this and what methods I'm supposed to use? I'm unsure of how I'm supposed to reach the answers.
These are the questions and these are the answers Any help is appreciated, thank you very much!

2. ## Re: How do I Graph the First and Second Derivative of a Function with no Equation?

Basically you are supposed to use your eyeballs and an understanding of the derivative to sketch $v(t)$ and then apply the same to $v(t)$ to sketch $a(t)$

First identify regions where the slope of the graph is fairly constant and sketch the derivative of those areas, it will be a constant.

Then note the behavior of the slope in the areas that are left, generally it's going to flip sign going through zero at some point.

Here's a rough sketch of #1 velocity is the thin blue line

acceleration is the thicker blue line

a more accurate sketch wouldn't have the sharp corners