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Math Help - Majorant and minorant

  1. #1
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    Unhappy Majorant and minorant

    Hi , Need some help plz :
    Find out the minimum on |R of the following functions :

    a - f: x --> 1 + |x| + 2x.
    b - g:x --> |x+1| - 4.

    Find out the maximum on |R of the following functions :

    a- h: x--> (1/|x|+3) +1.
    b- K: x--> (2/1+x) - 3.
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  2. #2
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    Re: Majorant and minorant

    Quote Originally Posted by Narimen View Post
    Hi , Need some help plz :
    Find out the minimum on |R of the following functions :

    a - f: x --> 1 + |x| + 2x.
    b - g:x --> |x+1| - 4.
    To #a): 1+2x^2>0 and is continuously increasing for all x \in \mathbb{R}. So the minimum of the complete term occurs when |x| has it's minimum.

    T #b): Similar argumentation as described at #a).

    Find out the maximum on |R of the following functions :

    a- h: x--> (1/|x|+3) +1.
    b- K: x--> (2/1+x) - 3.
    I don't understand the writing of the term at #a). Do you mean:

    h(x)=\frac1{|x|+3}+1 or h(x)=\left(\frac1{|x|}+3\right)+1

    To #b): The maximum of the complete term occurs when the fraction has it's maximum. Since the numerator is a constant the maximum is reached if the denominator has it's minimum. Since x is positiv or zero the minimum of the denominator is obvious.
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