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

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In summary, the conversation discusses the use of a graph and derivatives to determine the number of real solutions of an equation in a given interval. The hints provided involve evaluating the function at certain points and analyzing the signs of the results. The conversation also mentions a question that involves multiple choices, but this information is not necessary for understanding the main topic of the conversation.
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Let k be the number of real solutions of the equation e[tex]^{x}[/tex] + 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.
 
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  • #2
Hint: If f(x) = ex + x - 2, look at f(0), f(1) and f '(x).
 
  • #3
I know what f(0) and f(1) are and f '(x) = e[tex]^{x}[/tex] + 1

How is that suppose to help?
 
  • #4
Dustinsfl said:
I know what f(0) and f(1) are and f '(x) = e[tex]^{x}[/tex] + 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. :confused:
 
  • #5
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.
 
  • #6
Dustinsfl said:
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?
 
  • #7
The question said which of the following. I didn't need someone to tell me which one it was so I left it out.
 

1. What is the GRE Practice Question?

The GRE Practice Question is a standardized test used for admissions into graduate and business schools. It measures verbal reasoning, quantitative reasoning, and analytical writing skills.

2. How do I prepare for the GRE Practice Question?

Preparing for the GRE Practice Question involves familiarizing yourself with the test format and content, practicing with sample questions, and developing test-taking strategies. Many test prep companies also offer study materials and courses to help you prepare.

3. How long is the GRE Practice Question?

The GRE Practice Question is approximately 3 hours and 45 minutes long, with six sections including an optional break. The test is administered on a computer and can be taken at designated testing centers.

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You can register for the GRE Practice Question online through the official website of the Educational Testing Service (ETS). You will need to create an account, select a test date and location, and pay the registration fee. It is recommended to register at least 3-4 months in advance to secure your preferred test date and location.

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