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If $f(x)=x^2$ and $g(x)=2\sin x$ then what is the value of $||f-g||_{\infty}=$max$|f(x)-g(x)|$ how can i get value of x where difference of such function has maximum value?

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    Try taking the derivative and finding where the max/mins occur. You can determine it from this point (but if the interval is unbounded, it should be clear that it is $\infty$.2012-12-16
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    Max over what interval?2012-12-16
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    $g$ is bounded but $f$ is not. What does that tell you?2012-12-16
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    Taking the derivative is not really appropriate here (apart from minor details like differentiability which can be handled by squaring); you need to establish that a maximum exists first. Setting the derivative to zero will, at best, locate a local maximum in $[0,\frac{1}{2}]$.2012-12-16
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    As explicitely asked by @JohnD: **over which interval**? For the most natural choice, there is no maximum.2012-12-16
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    @JohnD interval is [0,1]2012-12-17

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