# 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?

Staff - 2 years, 9 months ago

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

Thanks for your reply, by the way.

- 2 years, 9 months ago

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?

Staff - 2 years, 9 months ago