Visualizing the Family of Anti-Derivatives

How to Use the GeoGebra Applet?

Uncheck and Check the Derivatives Toggle the visibility of the derivatives to explore their relationships with the functions.
Add Another Antiderivative of a Derivative Try adding a new antiderivative of the given derivative to see how different constants affect the function.
Understand the Original Function (Up to a Constant) Observe how the antiderivative recovers the original function, differing only by a constant.
Answer the Self-Assessment Questionnaire Test your understanding by completing the self-assessment questionnaire based on the applet’s functionality.

Why is f(x) the general family of antiderivatives?

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A
A. It represents the set of all possible functions whose derivative is f′(x)=2x, differing only by a constant.
B
B. It is the specific function for the derivative f′(x)=2x.
C
C. It is the only function whose derivative is f′(x)=2x.
D
D. It is the derivative of all functions with a constant term.

Why is g(x) an antiderivative of f(x)?

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What is the input when finding the antiderivative of g(x)?

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What is the output when finding the antiderivative of g(x)?

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Why do we have many antiderivatives of the derivatives represented by the linear function?

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A
A. Because the process of finding an antiderivative introduces an arbitrary constant, so we have a family of functions.
B
B. Because the linear function has an infinite number of derivatives.
C
C. Because the derivative of a function always results in a constant.
D
D. Because we can ignore the constant term in the antiderivative.