Solve GRE Practice Question: e^x + x - 2 = 0 in [0,1] with Graph Analysis

[Dustinsfl]

Let k be the number of real solutions of the equation e^{x} + x - 2 = 0 in the interval [0,1] and let n be the number of real solutions that are not in the interval.

By looking at the graph, I know it crosses the x axis; however, I don't remember or know how to do this problem.

 

[LCKurtz]

Hint: If f(x) = e^x + x - 2, look at f(0), f(1) and f '(x).

 

[Dustinsfl]

I know what f(0) and f(1) are and f '(x) = e^{x} + 1

How is that suppose to help?

 

[LCKurtz]

I know what f(0) and f(1) are and f '(x) = e^{x} + 1

How is that suppose to help?

You mean "supposed" to help.

What does the fact that f(0) and f(1) have opposite signs tell you? What does having a positive derivative tell you? And, of course, I'm just assuming I know what your actual question was since your original post doesn't actually contain a question.

 

[Dustinsfl]

At least this isn't an English forum. The question was in regards to multiple choices so I left that out because it wasn't needed.

 

[LCKurtz]

At least this isn't an English forum. The question was in regards to multiple choices so I left that out because it wasn't needed.

No extra charge for the English.

How are we supposed to know what the question was if you don't tell us? So, what was the question? And did the hints I gave you help you solve it?

 

[Dustinsfl]

The question said which of the following. I didn't need someone to tell me which one it was so I left it out.