Science:Math Exam Resources/Courses/MATH101 A/April 2024/Question 16 (b)
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Question 16 (b) |
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Consider the separable differential equation (b) A certain solution satisfies For this solution, what is the smallest value of over all real ? |
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? |
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! |
Hint |
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To find the specific solution, plug and into the general solution you found in part (a). Then find the smallest value that this specific solution takes. |
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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In part (a), we found the general solution To find the value of such that , plug in and : The result is . Therefore, the particular solution is . Now we must find the smallest value that this solution takes. By completing the square, the exponent is equal to , which is minimized when . Therefore, the smallest value takes is . |