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Find x which minimizes `f(x)=x - sqrt(1-x^2)`

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Find x which minimizes `f(x)=x - sqrt(1-x^2)`

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Posted (Answer #1)

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Given `f(x)=x-sqrt(1-x^2)`



At maximum or minimum,`f'(x)=0`

so, `1+x/sqrt(1-x^2)=0`

`rArr x/sqrt(1-x^2)=-1`


squaring both sides, we get


`rArr 2x^2=1`

`rArr x^2=1/2`

`rArr x=+-1/sqrt2`

When, `x=1/sqrt2`








Therefore, f(x) is minimum at `x=-1/sqrt2`


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handsofgod's profile pic

Posted (Reply #1)

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omg that's so simple, i just thought too hard

thank you sir


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