How do i solve this equation without graphing on a computer or calculator:
(e^x)+x-2=0
?
This equation appears on GRE 0568, #4)
Thanks.
GRE 0568 #4)
Re: GRE 0568 #4)
Consider continuous function
f(x) = exp(x) + x - 2.
Its derivative is always positive. Hence, the function is monotonous, increasing and, as result, might have only one root. Secondly,
f(0) = -1 < 0;
f(1) = e - 1 > 0.
Hence, its only root is inside interval [0, 1].
f(x) = exp(x) + x - 2.
Its derivative is always positive. Hence, the function is monotonous, increasing and, as result, might have only one root. Secondly,
f(0) = -1 < 0;
f(1) = e - 1 > 0.
Hence, its only root is inside interval [0, 1].