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Math Help - maxium at a point

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    maxium at a point

    17. Define by f(x) = 1/(1 + x2). Prove that f has a maximum and find the point at which that maximum occurs.

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    Quote Originally Posted by lacy1104 View Post
    17. Define by f(x) = 1/(1 + x2). Prove that f has a maximum and find the point at which that maximum occurs.

    Thanks
    Since \forall x \in  \mathbb{R}, x^2 \geq 0 \text{ Equality at x=0}

    \Rightarrow 1+x^2 \geq 1 \text{ Equality at x=0}

    \Rightarrow \frac1{1+x^2} \leq 1 \text{ Equality at x=0}

    Thus f(x) is bounded above by 1(its also the lub and hence the maxima).
    We also see that maxima occurs at 0.
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