# Determine derivative of polynomial from graph on a multiple choice question [closed]

On a multiple choice question I need to determine which of the following graphs:

Multiple choice graphs

When derivated, yields:

The graph

Is there a general, fastest way to solve this kind of questions?

My math is rusty and I'm trying to catch up.

## closed as off-topic by Cameron Williams, max_zorn, Jyrki Lahtonen, Jendrik Stelzner, YuiTo ChengMay 26 at 8:03

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• To start, I'd encourage you to think about the ranges for which the slope is positive, negative, and zero, as well as how the slopes themselves change in these regions. – cmk May 25 at 21:28
• In this case, the graph of the derivative shows that it has two zeros, at both of which it changes sign. The original function must therefore have turning points at precisely those two points and nowhere else. This alone is enough to rule out all but one of the multiple choice graphs. Even so, I'd suggest you follow cmk's advice as way of confirming your answer. – lonza leggiera May 25 at 23:00
• Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For typesetting, please use MathJax. – dantopa May 26 at 2:19
• This is not a trivial question. I hope it gets answered. – NoChance May 26 at 12:12