Matematické Fórum

stuart clark · 26. 05. 2011 05:03

If $f(x) = -1+kx+k$ neither touch or nor intercepts the curve $f(x) = ln(x),$ then minimum value of $k\in$

musixx · 26. 05. 2011 08:59

Local extrem of a function $g(x)=kx+k-1-\ln(x)$ is realized in $x=\frac1k$ , and its value is $k+\ln(k)$ , which is zero for $k=W(1)$ (Lambert W-Function). Therefore $k\in(W(1),\infty)$ .

$W(1)\dot=0.567143$

Matematické Fórum

#1 26. 05. 2011 05:03

minimum value of k

#2 26. 05. 2011 08:59

Re: minimum value of k

Zápatí