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Antiderivatives

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There are two incircled questions attached.

The graph of a function of f is shown. Which graph is an antiderivative of f and why?
Find the antiderivative F of f that satisfies the given condition.

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https://brainmass.com/math/real-analysis/antiderivative-graph-213692

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Solution Summary

The solution provides an example of finding an antiderivative and identifying the graph of the antiderivative.

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Problems with Antiderivatives

Determine the value of a that makes F(x) an antiderivative of f(x)
f(x)=9square root x , F(x)=ax^3/2

Please provide any tricks I can use to remember steps to these kinds of problems.

Find antiderivatives of the given function.
f(x)=4/3x^1/3

Please show step by step and example any rules that need to be remembered.

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