How can I use this?

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!

Note by Shashank Rammoorthy
2 years, 9 months ago

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Yes 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?

Calvin Lin Staff - 2 years, 9 months ago

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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.

Shashank Rammoorthy - 2 years, 9 months ago

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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.

  • Coordinate geometry, finding tangent of parabola
  • Min/Max of convex functions occur at tangent

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

Calvin Lin Staff - 2 years, 9 months ago

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