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If ey = X1/x then y has a
- a)Maximum at x = e
- b)Minimum at x = e
- c)Maximum at x = e-1
- d)Minimum at x = e-1
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If ey = X1/x then y has aa)Maximum at x = eb)Minimum at x = ec)Maximum...
Understanding the Function
The given function is expressed as ey = X1/x. To analyze this function for maximum and minimum points, we need to find the critical points by taking the derivative and setting it to zero.
Finding the Derivative
1. Differentiate the function ey = X1/x with respect to x.
2. This will give us dy/dx, which helps identify critical points.
Critical Points
- Set dy/dx = 0 to find the critical points. This is essential because the maximum or minimum occurs where the slope of the function is zero.
Second Derivative Test
1. Calculate the second derivative, d²y/dx².
2. Evaluate the second derivative at the critical points found earlier.
Analyzing the Results
- If d²y/dx² < 0,="" the="" function="" has="" a="" local="" />
- If d²y/dx² > 0, the function has a local minimum.
Conclusion
In this case, the correct answer is option 'A', indicating that y has a maximum at x = e.
- This means that when x equals e, the value of the function reaches its highest point, confirming that it is a maximum.
Key Takeaway
Understanding the behavior of the function through derivatives is crucial for determining maxima and minima. The critical point analysis and the second derivative test are vital tools in this process, leading to the conclusion that y has a maximum at x = e.
The given function is expressed as ey = X1/x. To analyze this function for maximum and minimum points, we need to find the critical points by taking the derivative and setting it to zero.
Finding the Derivative
1. Differentiate the function ey = X1/x with respect to x.
2. This will give us dy/dx, which helps identify critical points.
Critical Points
- Set dy/dx = 0 to find the critical points. This is essential because the maximum or minimum occurs where the slope of the function is zero.
Second Derivative Test
1. Calculate the second derivative, d²y/dx².
2. Evaluate the second derivative at the critical points found earlier.
Analyzing the Results
- If d²y/dx² < 0,="" the="" function="" has="" a="" local="" />
- If d²y/dx² > 0, the function has a local minimum.
Conclusion
In this case, the correct answer is option 'A', indicating that y has a maximum at x = e.
- This means that when x equals e, the value of the function reaches its highest point, confirming that it is a maximum.
Key Takeaway
Understanding the behavior of the function through derivatives is crucial for determining maxima and minima. The critical point analysis and the second derivative test are vital tools in this process, leading to the conclusion that y has a maximum at x = e.
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If ey = X1/x then y has aa)Maximum at x = eb)Minimum at x = ec)Maximum...
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