Assignment question, root, Intermediate Value Theorem

In summary, the problem asks to use the Intermediate Value Theorem to prove that the equation 3 arctan(2x-1)=cos^2(x-(∏/6)) + 1 has at least one positive real root. The student expresses difficulty in solving the problem due to recent ADHD diagnosis and medication. The Intermediate Value Theorem states that if a continuous function takes on two values at two different points, then it must also take on any value between those points.
  • #1
kuttaman
4
0

Homework Statement



Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function.

3 arctan(2x-1)=cos^2(x-(∏/6)) + 1

Homework Equations



No clue

The Attempt at a Solution



I honestly speaking have no clue how to even start on this question, I have studied the text but my brain right now is just no functioning. I recently got diagnosed with ADHD and recentlyu started the medication (2days ago) so my head is a little sluggish and fatigued. Math is a bit of a thinking game, and this question is very detrimental for me to get. If someone can answer this/ or help me answer this it would be highly appreciated.
 
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  • #2
kuttaman said:

Homework Statement



Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function.

3 arctan(2x-1)=cos^2(x-(∏/6)) + 1

Homework Equations



No clue

The Attempt at a Solution



I honestly speaking have no clue how to even start on this question, I have studied the text but my brain right now is just not functioning. I recently got diagnosed with ADHD and recently started the medication (2days ago) so my head is a little sluggish and fatigued. Math is a bit of a thinking game, and this question is very detrimental for me to get. If someone can answer this/ or help me answer this it would be highly appreciated.
What does the Intermediate Value Theorem state ?
 

Related to Assignment question, root, Intermediate Value Theorem

1. What is an assignment question?

An assignment question is a question given to students as part of an assignment or homework. It usually requires the student to apply their knowledge and skills to solve a specific problem or demonstrate their understanding of a particular concept.

2. What is a root in mathematics?

In mathematics, a root is a number that, when multiplied by itself a certain number of times, will result in a given number. For example, the square root of 25 is 5 because 5 multiplied by itself (5x5) equals 25.

3. What is the Intermediate Value Theorem?

The Intermediate Value Theorem is a mathematical theorem that states that if a continuous function has different values at two points, it must have at least one point where it takes on every value between those two points.

4. How is the Intermediate Value Theorem used in mathematics?

The Intermediate Value Theorem is used in mathematics to prove the existence of roots or solutions to equations. It is also used to prove the existence of points where a function takes on a specific value within a given interval.

5. Can the Intermediate Value Theorem be applied to all functions?

No, the Intermediate Value Theorem can only be applied to continuous functions. A continuous function is one that has no breaks or gaps in its graph and can be drawn without lifting the pen from the paper. Functions that have discontinuities or jumps cannot be analyzed using the Intermediate Value Theorem.

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