Is there a way I could use the derivative of a polynomial \(f(x)\), i.e, finding the slope of \(f(x)\) at a given or any \(x\) to solve polynomial problems, like the problems that show up in math olympiads and tests?

Thank you!

Is there a way I could use the derivative of a polynomial \(f(x)\), i.e, finding the slope of \(f(x)\) at a given or any \(x\) to solve polynomial problems, like the problems that show up in math olympiads and tests?

Thank you!

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TopNewestYes of course, there are lots of ways of doing so. For example, if you want to find the coefficient of the linear term, evaluate \( f'(0) \).

What other ways can you think of?

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I dunno...how else could I use the slope of the graph of the polynomial?

Thanks for your reply, by the way.

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Yes, finding the slope of a graph is a good way to think about possible uses. Here are a few more suggestions.

What else? What else are derivatives used in? How else can we use them?

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