How to find the minimum from this equation?

Question

By using calculus how to find the exact values of x?

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Answer 1 · 2018-05-18T08:34:39

See process below

Let $f (x) = \frac{x}{\sqrt{x^{2} + 100}} - \frac{1}{4}$ $f(x)=x/sqrt(x^2+100)-1/4$

To find the minimum we evaluate $f´(x)=0$

$f´(x)=(2x^2-100)/(x^4+200x^2+10000·sqrt(x^2+100)$

This function will be zero if $2x^2-100=0$

Then $x=+-sqrt50$