suppose we we have following equations and conditions Let $k$ be the number of real solutions of the equation $e^x+x-2=0$ in the interval $[0, 1]$ and and let $n$ be the number of real solutions that are not in $[0,1]$ Which of the following is true?
$k=0$ and $n=1$
$k=1$ and $n=0$
first of all what i have tried is this:if we differentiate we get following thing $e^x=-1$ but how it is possible?,using wolfram alpha i got this result
but how to prove it using mathematical procedure?have to i use newtons method for compute actual root or there is some specific theorem which helps me to determine it more easily?