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Math Help - Proof of No Local Max/Min

  1. #1
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    Proof of No Local Max/Min

    Okay.. so I've been doing calculus for about 4 hours at this point. And I haven't the slightest clue how to go about this proof... and my brain feels like jello.

    Prove that the function

    f(x)=x^{101}+x^{51}+x+1

    has neither a local maximum nor a local minimum.

    I took the derivative and now do not have any clue of what I need to do... how can I find critical points for it? Please help.

    f'(x)=101x^{100}+51x^{50}+1
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by banshee.beat View Post
    Okay.. so I've been doing calculus for about 4 hours at this point. And I haven't the slightest clue how to go about this proof... and my brain feels like jello.

    Prove that the function

    f(x)=x^{101}+x^{51}+x+1

    has neither a local maximum nor a local minimum.

    I took the derivative and now do not have any clue of what I need to do... how can I find critical points for it? Please help.

    f'(x)=101x^{100}+51x^{50}+1
    notice that this is actually a quadratic in disguise. it is quadratic in x^{50}. if you can't see it, let a = x^{50}, then you have 101a^2 + 51a + 1

    now can you find the critical points? set the function to zero and see what happens
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