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# The graphs of $f$ and $f^{\prime}$ each pass through the origin. Use the graph of $f^{\prime \prime}$ shown in the figure to sketch the graphs of $f$ and $f^{\prime} .$ To print an enlarged copy of the graph, go to the website www. mathgraphs.com.

## $f^{\prime \prime}(x)=\sqrt[3]{x}$$f^{\prime}(x)=\frac{3}{4} x^{\frac{4}{3}}$$f(x)=\frac{9}{28} x^{\frac{7}{3}}$

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eso What I would do to figure out this problem is the graph looks like as they give it to you of the second derivative of X of F, I should say is equal to the cube root of X. But I would just write his ex to the one third power. So if you are test, then figure out what the anti derivative of that is. But you can do that by adding one to the experiment and then multiply by the reciprocal. And if you take that into why equals, um into a graphing calculator, this will tell you the graph. This will show you the graph. I should say, um, we have to do that of the first derivative because the anti drove the world Cancel that out now. You could also do a plus C in there if you wanted Thio and you could just shift the graph up and down because that's sort of the nice thing about thes anti derivatives is there's a new infinite number of answers. So then, if you were then finding the anti directive of that function again, add one to your exponents, so that's now seven thirds and multiply by the reciprocal of that well, three times through nine, four times seven is 28 because you're marrying Multiply, um, fractions, you know, straight across. So if you take this into a graphing calculator, it would give you a graph of F FX, and again you could do a plus C in there. But it's unnecessary, basically everything you need to know about this problem, so

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The text passage contains a mathematical question related to graphing functions and their derivatives, and it provides the answers to the functions in the form of equations.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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# The graphs of $f$ and $f^{\prime}$ each pass through the origin. Use the graph of $f^{\prime \prime}$ shown in the figure to sketch the graphs of $f$ and $f^{\prime} .$ To print an enlarged copy of the graph, go to the website www. mathgraphs.com.

## $f^{\prime \prime}(x)=\sqrt[3]{x}$$f^{\prime}(x)=\frac{3}{4} x^{\frac{4}{3}}$$f(x)=\frac{9}{28} x^{\frac{7}{3}}$

Integration

### Discussion

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Lectures

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### Video Transcript

eso What I would do to figure out this problem is the graph looks like as they give it to you of the second derivative of X of F, I should say is equal to the cube root of X. But I would just write his ex to the one third power. So if you are test, then figure out what the anti derivative of that is. But you can do that by adding one to the experiment and then multiply by the reciprocal. And if you take that into why equals, um into a graphing calculator, this will tell you the graph. This will show you the graph. I should say, um, we have to do that of the first derivative because the anti drove the world Cancel that out now. You could also do a plus C in there if you wanted Thio and you could just shift the graph up and down because that's sort of the nice thing about thes anti derivatives is there's a new infinite number of answers. So then, if you were then finding the anti directive of that function again, add one to your exponents, so that's now seven thirds and multiply by the reciprocal of that well, three times through nine, four times seven is 28 because you're marrying Multiply, um, fractions, you know, straight across. So if you take this into a graphing calculator, it would give you a graph of F FX, and again you could do a plus C in there. But it's unnecessary, basically everything you need to know about this problem, so

Integration

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user
The text passage contains a mathematical question related to graphing functions and their derivatives, and it provides the answers to the functions in the form of equations.

TYPE: SINGLE_QUESTION_WITH_ANSWER