I on the graphs of antiderivatives

[franz32]

Hello everyone. I need help.

If there are given 2 graphs in which one of them is the graph of the derivative of the other graph (that graph is the antiderivative - the "original" one), how can I tell the graph of a derivative from a graph of an antiderivative?

In another case: the graph of the derivative is given with some necessary
information for the graph of the unknown - antiderivative... how can I
figure out that required graph of the anitderivative from the given clues?

 

[Muzza]

I don't know any surefire way, but the first thing I'd look at would be the roots of the functions. The derivative will have a root (i.e be zero) where the original function "is horizontal". Also, it should be easier if the graphs depict polynomials (let's say you're given something that looks like a cubic, and a parabola. The cubic is obviously the original function, since the derivative of a cubic is a parabola...).

 

[Gokul43201]

Just look at the slope. If the original function is sloping upwards the derivative will be > 0 (above the x-axis)...and when it turns downwards, the derivative falls below te x-axis. And as muzza said, where the function is going through a peak or trough, the derivative will cut across the x-axis. Also, if there are numbers on the x- and y-axes, you can approximate some short section of the function to a straight line and find its slope. This should be the rough value of the derivative function at the same x-value.