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Math Help - A question about curve sketching and imaginary numbers

  1. #1
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    A question about curve sketching and imaginary numbers

    Hello.

    I was wondering, what does it mean in terms of graphing when I bump into "i" during curve sketching? For example, in this particular "sketch the curve" question, in my check for extrema points I'm getting x to be an imaginary number:





    first derivative check for maxs and mins:



    or

    Does this just mean no max or min exists?
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  2. #2
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    Quote Originally Posted by shawli View Post
    Hello.

    I was wondering, what does it mean in terms of graphing when I bump into "i" during curve sketching? For example, in this particular "sketch the curve" question, in my check for extrema points I'm getting x to be an imaginary number:





    first derivative check for maxs and mins:



    or

    Does this just mean no max or min exists?
    Yes. Notice that the derivative is negative everywhere it's defined, so the function is decreasing everywhere.
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  3. #3
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    Quote Originally Posted by shawli View Post
    Hello.

    I was wondering, what does it mean in terms of graphing when I bump into "i" during curve sketching? For example, in this particular "sketch the curve" question, in my check for extrema points I'm getting x to be an imaginary number:





    first derivative check for maxs and mins:



    or

    Does this just mean no max or min exists?

    Of course. The function is a real one so its derivative never vanishes within the real numbes and thus there are no extreme points. In fact, f'(x)<0 \,\,\forall x \in \mathbb{R} so this is a monotonically descending function and, thus again, without extreme points.

    Tonio
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