text: Friday
  May 6, 2016
  
  # Homework Help: math
  
  Posted by sonya on Thursday, January 24, 2008 at 6:32pm.
  
  x^3-4x-2 [2,3]
  
  we have to use the intermediate value thereom. not sure how to do this.
  • math - Damon, Thursday, January 24, 2008 at 7:30pm
  
  x^3-4x-2 [2,3]
  the function is continuous between 2 and 3
  at 2 f(2) = -2
  at 3 f(3) = +13
  
  The theorem states that for every number N between -2 and +13, there is some x between 2 and 3 such that f(x) = N
  
  Now they did not give you an N so I will say 5 for example is between -2 and +13
  
  The theorem says that some x between 2 and 3 will come out with f(x)= 5
  
  I would have to solve it by trial and error but I know to start between 2 and 5
  x f(x)
  2 -2
  
  try 2.5 --> 3.63 too small
  try 2.7 --> 6.88 too big
  try 2.6 --> 5.18 closer, a bit big
  try 2.58 -> 4.85 a little small
  try 2.585-> 4.93 well you get the idea
  
  3 13
  
  The theorem says that
explanation: The document contains a math question and an answer. The question is about using the Intermediate Value Theorem to determine if there is a value of \( x \) between 2 and 3 for which \( f(x) = 5 \) for the function \( f(x) = x^3 - 4x - 2 \). The answer provides a detailed explanation of how to apply the theorem and includes a step-by-step process to find the value of \( x \) that satisfies the condition.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Friday
  May 6, 2016
  
  # Homework Help: math
  
  Posted by sonya on Thursday, January 24, 2008 at 6:32pm.
  
  x^3-4x-2 [2,3]
  
  we have to use the intermediate value thereom. not sure how to do this.
  • math - Damon, Thursday, January 24, 2008 at 7:30pm
  
  x^3-4x-2 [2,3]
  the function is continuous between 2 and 3
  at 2 f(2) = -2
  at 3 f(3) = +13
  
  The theorem states that for every number N between -2 and +13, there is some x between 2 and 3 such that f(x) = N
  
  Now they did not give you an N so I will say 5 for example is between -2 and +13
  
  The theorem says that some x between 2 and 3 will come out with f(x)= 5
  
  I would have to solve it by trial and error but I know to start between 2 and 5
  x f(x)
  2 -2
  
  try 2.5 --> 3.63 too small
  try 2.7 --> 6.88 too big
  try 2.6 --> 5.18 closer, a bit big
  try 2.58 -> 4.85 a little small
  try 2.585-> 4.93 well you get the idea
  
  3 13
  
  The theorem says that
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and an answer. The question is about using the Intermediate Value Theorem to determine if there is a value of \( x \) between 2 and 3 for which \( f(x) = 5 \) for the function \( f(x) = x^3 - 4x - 2 \). The answer provides a detailed explanation of how to apply the theorem and includes a step-by-step process to find the value of \( x \) that satisfies the condition.
  
  Label: question-and-answer