How do you graph the derivative when given the graph of the initial equation but doesn't state the equation?

The derivative is the slope of the graph at any given point. If you have a graph that is full of straight line segments, the derivative of that graph will be a bunch of horizontal line segments with open circle endpoints. For example if part of graph was a line segment from (0,0) to (2,2) we would know the slope between 0 and 2 on the x axis would be 1. So, the graph of the derivative between 0 and 2 would be a horizontal line segment with open endpoints at y = 1 from 0 to 2.

This post was edited by timmayX on Mar 8 2016 02:23am

or you could think of a function that replicates what the graph shows, take it's derivative, then graph it.

It's impossible, unless :
- you know with an infinite precision the position of any point of the initial graph (which in turns is almost the same as knowing the equation)
- you know something extra about the graph regularity, that allows you to give a valid approximation of the derivative.

See that counter-example :

f ( x ) = 100 + 0.01. cos (10000.x )

Show the graph of f : it appears like an horizontal straight line. You might believe that its derivative is zero.
Now check with the given equation, and see what happens.

feanur is correct (of course), but there is lots of shitty math questions out there. So if you are given what looks like the graph of x^2 and they ask you for the derivative, write down 2x.