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Thread: graphing question help

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    graphing question help

    for the relation x^3 + y^3 =1

    a) find the x and y intercepts
    do I factorise to (x-1)(x^2 + x +1)
    now what?

    b) findthe axis of symmetry by exchanging x and y

    c) differentiate implicitly and find the stationary and critical point/s

    d) discuss the behaviour of the curve as x tends to plus/minus infinity

    thank you!!

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    Re: graphing question help

    for a) it is right you factorise (x-1)(x^2+x+1) and the result would be x = 1
    for b) the question literally means swayp x and y values, like
    x^3+y^3=1 --> y^3+x^3=1 this proves them to be diagonally symmetrical
    for c) its just implicit deifferentiation which results out to be = -x^2/y^2 and simply find the TP and POI
    for d) its simple take limits to pos and neg infinity

    If you need worked out example, im happiliy willing to do them, just ping me if you dont understand a question specifically
    Last edited by HeroWise; 7 Jan 2018 at 3:10 PM.
    sssona09 likes this.

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    Re: graphing question help

    Quote Originally Posted by HeroWise View Post
    for a) it is right you factorise (x-1)(x^2+x+1) and the result would be x = 1
    for b) the question literally means swayp x and y values, like
    x^3+y^3=1 --> y^3+x^3=1 this proves them to be diagonally symmetrical
    for c) its just implicit deifferentiation which results out to be = -x^2/y^2 and simply find the TP and POI
    for d) its simple take limits to pos and neg infinity

    If you need worked out example, im happiliy willing to do them, just ping me if you dont understand a question specifically
    thank you for the help!!! <3
    Last edited by sssona09; 7 Jan 2018 at 4:23 PM.

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    Re: graphing question help

    so do I make dy/dx =0 -----> I found the SP to be (0,1)

    do I now find inflection point

    edit: solved
    Last edited by sssona09; 7 Jan 2018 at 4:23 PM.

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    Re: graphing question help

    Critical points include Inflexion too ;P
    NOTE to OP: ik u solved it but just for people who might find this info useful
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    Re: graphing question help

    Quote Originally Posted by HeroWise View Post
    Critical points include Inflexion too ;P
    NOTE to OP: ik u solved it but just for people who might find this info useful
    Critical points of a differentiable function should just be points where the first derivative is 0. You may want to consult your textbook to see what definition it gives for a critical point.

    Wikipedia: https://en.wikipedia.org/wiki/Critic..._(mathematics)
    sssona09 likes this.

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