Give an example of a function which has a derivative of 0 at x = 0 (not use a constant function)?

had this question on an online quiz, and had no idea what to put. this is the explanation it gave: "There are infinitely many solutions.

To give an example of a function that has a slope of 0 at x = 0, it's probably best to think about the graphs of some simple functions that might work -- remember that a slope of 0 means that your function should have a horizontal tangent at x = 0"

but I'm still confused, could someone give me a few examples or explain it differently? thanks

4 Answers

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  • 4 weeks ago

    For a more complicated function, try this:

    y' = 5x^4 + 4x^3+ 2x

    Therefore,

    y = x^5 + x^4 + x^2 + constant

  • 4 weeks ago

    f(x) = x^2, a parabola has a derivative equal to 0 at x = 0.  Clearly, the slope of a tangent line at that point would be horizontal.

    f(x) = cos(x) is another example.

  • alex
    Lv 7
    4 weeks ago

    y = x²          

  • 4 weeks ago

    How about something simple like this?

    y = x²

    It's a parabola with its vertex at (0,0). At the vertex of a parabola, the slope is zero.

    Other answers that would work:

    y = x² + 1

    y = x^3

    y = x^4 - 64

    y = 2x^5

    y = cos x

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