how do i sketch the derivative function of a graph of a given function?

Question

i know how to find derivative of a point easy. im thrown by not being given any function im just shown a graph, so do i figure out what the function of the graph is? im looking through my book and having trouble finding how to do it. do i take multiple points and find the derivative at each one then graph it? im soo lost please help.

thanks

i know but it says nothing about what the function is. it is just a graph of a function. if i knew the function id be less confused but its just a graph of a function and does not say what is is.

Answer 1

By differentiating you will get a function. So just sketch it.
For example is y=x^2 then y'=2x we have a straight line. That is it. Note that the derivative will have positive slope for x > 0 and negative slope for x<0. It was anticipated. Was it not?

Answer 2

Using the gradient curve you can see when the graph is increasing (gradient is positive) and by how much; when it is decreasing (gradient is negative) and how sharply; and also identify the turning points when the gradient curve cuts the x-axis (ie is zero). But the original function can shift vertically up or down. You can't locate the original function in this direction from the gradient. Ofsourse if you have the derivative, you could just integrate! and viola, there's the original function. (The constant of integration +c is the vertical shift mentioned above). Hope this helps!

Answer 3

I would just look at each part of the graph, and decide if the slope for each part is positive high (call it +3), positive medium (+2), positive low (+1), about zero (0), negative low (-1), negative medium (-2), or negative high (-3). That way, you only need to decide if the slope is positive or negative, and if it is very steep, moderately steep, gentle, or level.

Then sketch/draw the values, over the range +3 down to -3.