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Math Help - Another Curve Sketching question

  1. #1
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    Another Curve Sketching question

    Hi, sorry to post another question about curve sketching (this is my last one) but I am having difficulties with the following function:

    f(x) = cosx - sinx

    If someone could provide a sketch of what this function looks like that would be great, that way I have something to work towards. I've done all the calculus work but I'm having a real hard time making sense of it.

    I have:

    - the y-int: y=1
    - the zeros: x=(pi)/4 and 5(pi)/4
    - niether odd or even
    - no asymptotes
    - increasing everywhere (I'm really not sure if that is right)
    - no local max/min
    - concave down everywhere (I'm also not sure if that is right)
    - no inflection points

    I've had no luck graphing this so I'm sure I've made a big mistake somewhere. Any help at all would be great!

    Thanks.
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  2. #2
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    Quote Originally Posted by pbfan12 View Post
    Hi, sorry to post another question about curve sketching (this is my last one) but I am having difficulties with the following function:

    f(x) = cosx - sinx

    If someone could provide a sketch of what this function looks like that would be great, that way I have something to work towards. I've done all the calculus work but I'm having a real hard time making sense of it.

    I have:

    - the y-int: y=1 Mr F says: Correct

    - the zeros: x=(pi)/4 and 5(pi)/4 Mr F says: Partly correct .... You can obviously add multiples of 2 \pi to each of these to get more zeros.

    - niether odd or even Mr F says: Correct

    - no asymptotes Mr F says: Correct

    - increasing everywhere (I'm really not sure if that is right)

    - no local max/min Mr F says: Wrong. How did you arrive at this conclusion? f^{'} (x) = 0 has an infinite number of solutions .......

    - concave down everywhere (I'm also not sure if that is right) Mr F says: It's not.

    - no inflection points Mr F says: Wrong. How did you arrive at this conclusion?

    I've had no luck graphing this so I'm sure I've made a big mistake somewhere. Any help at all would be great!

    Thanks.
    You should also consider that the domain is R and the range is .....?

    Life will be much much much easier for you if you express cosx - sinx in the form Acos(x - \phi). Do you know how to do this?
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