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Math Help - What is the smallest n for which...

  1. #1
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    What is the smallest n for which...

    On my latest assignment in high school calculus to do over the Spring Break, I've been given this problem: "What is the smallest n for which d^n(12x^3 + 2x) / dx^n = 0, for all x?" - I don't know where to start with this, but my teacher mentioned something about finding the derivatives. Can someone here please help point me in the right direction?
    Last edited by Newbie2; March 12th 2013 at 04:34 PM.
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  2. #2
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    Re: What is the smallest n for which...

    Well, find \frac{d}{dx}(12x^3 + 2x), \frac{d^2}{dx^2}(12x^3 + 2x), \frac{d^3}{dx^3}(12x^3 + 2x), ... and see when it becomes 0. Of course, you need to know what the definition of \frac{d^n}{dx^n}(12x^3 + 2x) is.
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  3. #3
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    Re: What is the smallest n for which...

    Quote Originally Posted by emakarov View Post
    Well, find \frac{d}{dx}(12x^3 + 2x), \frac{d^2}{dx^2}(12x^3 + 2x), \frac{d^3}{dx^3}(12x^3 + 2x), ... and see when it becomes 0. Of course, you need to know what the definition of \frac{d^n}{dx^n}(12x^3 + 2x) is.
    Now that you write it out like that, I now know exactly what the "d^n / dx^n" part meant and was able to solve the problem easily. Thanks!
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