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Thread: Characteristics of combined functions

  1. #1
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    Question Characteristics of combined functions

    Hi,

    I hope someone can help. I'm hoping that someone help me understand combined function characteristics with the following examples:

    1. y=2^x-x^3 would this function not have a relative maximum at x = 0.59? Would it also have a minimum at x = 8.177?
    2. y = sin(2pix) - 2sin(pix) my textbook says that the zero/x-intercept for this function is k. Which doesn't make any sense to me. Can someone please tell me whether this is correct to think that the zero is k?
    3. y = sin(2pix) + 2 + (1/x) my textbook says that this function has zeros that are changing at irregular intervals - however, I personally don't see where the function experiences any zeros in the first place. Am I understanding this correctly?
    4. y = sin(2pix) + 2 + (1/x) The textbook is also saying for the same function as the one above that the maximum and minimum values are at irregular intervals. I don't see how this is possible. Do you think that my textbook is referring to local maximum or minimum values?

    I know these are a lot of questions, but there wasn't a lot of information online that I could find to help me. Again, I really hope someone can help!

    Sincerely,
    Olivia
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  2. #2
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    Re: Characteristics of combined functions

    1. y=2^(x-x^3)
    I assume you mean $y = 2^{x-x^3}$ ... if so, enclose the entire exponent in parentheses

    relative max at $x \approx 0.577$, real min at $x \approx -0.577$


    2. y = sin(2pix) - 2sin(pix)
    $y = 2\sin(\pi x)\cos(\pi x) - 2\sin(\pi x) = 0$

    $2\sin(\pi x)[\cos(\pi x) - 1= 0 \implies x = k, \, k \in \mathbb{Z}$


    3 and 4. y = sin(2pix) + 2 + (1/x)
    $y = 0$ at $x = -\dfrac{1}{2}$

    yes, relative extrema
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    Re: Characteristics of combined functions

    Quote Originally Posted by otownsend View Post
    1. y=2^x-x^3 would this function not have a relative maximum at x = 0.59? Would it also have a minimum at x = 8.177?
    Quote Originally Posted by skeeter View Post
    I assume you mean $y = 2^{x-x^3}$ ...
    I am quite sure that it is as posted: $y=2^x-3x$ See here.
    One solution is $0.589665$
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    Re: Characteristics of combined functions

    Quote Originally Posted by Plato View Post
    I am quite sure that it is as posted: $y=2^x-3x$ See here.
    One solution is $0.589665$
    agree ... mea culpa
    Attached Thumbnails Attached Thumbnails Characteristics of combined functions-fmin1.png   Characteristics of combined functions-fmax1.png  
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    Re: Characteristics of combined functions

    Thanks for everyone's help. I understand now what I was confused about.
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