I on the graphs of antiderivatives

In summary, determining the graph of a derivative from a graph of an antiderivative involves looking at the roots of the functions and examining the slope. Additionally, if there are numbers on the x- and y-axes, one can approximate a section of the function to find its slope, which will be the approximate value of the derivative at that x-value.
  • #1
franz32
133
0
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?
 
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  • #2
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...).
 
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  • #3
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.
 

1. What is an antiderivative?

An antiderivative is a function that, when differentiated, gives the original function. It is the inverse operation of taking a derivative.

2. How do I find the antiderivative of a function?

To find the antiderivative of a function, you can use the reverse power rule, which involves increasing the power by 1 and dividing by the new power. You can also use integration techniques such as substitution, integration by parts, and partial fractions.

3. What is the difference between an antiderivative and an indefinite integral?

An antiderivative is a function that is the inverse operation of taking a derivative, while an indefinite integral is a family of functions that all have the same derivative. The constant of integration differentiates these functions.

4. How do I know if I have found the correct antiderivative?

To check if you have found the correct antiderivative, you can take the derivative of the function and see if it matches the original function. You can also use a graphing calculator to graph both the function and its antiderivative and see if they overlap.

5. How do I graph antiderivatives?

To graph antiderivatives, you can use a graphing calculator or plot points by finding the x and y values for different inputs. You can also use the constant of integration to graph different antiderivative functions within a family.

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