How do I graph an antiderivative?

[Masakiuma]

hey all
if I have the function for a derivative (which it is impossible to find an integral for, by the way), how do I graph the original?
This graph is shaped kind of like an M, meaning it has some sharp points...on the original graph, would these be asymptotes or also sharp points??
thanx in advance

 

[HallsofIvy]

Remember that the anti-derivative (the original function) is the area under the curve or, conversely, that the derivative is the slope of the curve.

And, of course, knowing the derivative only tells you the original function up to an additive constant. Choose some arbitrary starting height for your function- 0 will do.

As long as your derivative function is positive, you know that the original function is increasing and the larger the value of the derivative the greater slope of the orginal function. If you derivative graph looks like an "M" (starting at y'= 0?) then your original function will be a graph curved upward (concave upward) getting steadily steeper until the derivtive reaches a maximum. As your derivative graph comes back down from the maximum, the graph of the original curve will still go up but now becoming less steep until, when the derivative function is 0 again, the graph of the original curve is horizontal. The second half of the M repeats that- increasing from the new height of course.

 

[tacman]

To graph an antiderivative, you can use the fundamental theorem of calculus. This states that the antiderivative of a function is the original function. So, if you have a function for the derivative, you can simply integrate it to find the antiderivative and then plot it on a graph. The sharp points on the derivative graph will correspond to abrupt changes or discontinuities on the antiderivative graph. These points will not necessarily be asymptotes, as they could also be points of discontinuity or cusps. It is important to carefully consider the behavior of the derivative function in order to accurately graph the antiderivative. I hope this helps!