Limits Continuity And Differentiability

If a continuous functions \(f\) defined on the real line \(R\), assumes positive and negative values in \(R\) then the equation \(f(x)=0\) has a root in \(R\). For example, if it is known that a continuous function \(f\) on \(R\) is positive at some point and its minimum value is negative then the equation \(f(x)=0\) has a root in \(R\). Consider \(f(x)=k e^{x}-x\) for all real \(x\) where \(k\) is a real constant.

The line \(y=x\) meets \(y=k e^{\mathrm{x}}\) for \(k \leq 0\) at