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For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)?
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For x is greater than equal to 0, the smallest value of expression y=(...
Explanation:
The expression given is y = (3x² + 6x + 6) / 2(x + 1)
Finding the minimum value:
To find the smallest value of y for x greater than or equal to 0, we need to find the minimum value of the expression.
1. First Step:
Simplify the expression:
y = (3x² + 6x + 6) / 2(x + 1)
y = (3x² + 6x + 6) / 2x + 2
2. Second Step:
To find the minimum value, we need to find the derivative of y with respect to x and set it equal to 0.
dy/dx = (6x + 6) / 2(x + 1) - (3x² + 6x + 6) / (2(x + 1)²) = 0
3. Third Step:
Solve for x by equating the derivative to 0 and find the critical points.
4. Fourth Step:
After finding the critical points, determine which one corresponds to the minimum value by using the second derivative test.
5. Fifth Step:
Once the minimum value is found, substitute the value of x back into the expression to find the smallest value of y.
By following these steps, you can find the smallest value of the given expression for x greater than or equal to 0.
The expression given is y = (3x² + 6x + 6) / 2(x + 1)
Finding the minimum value:
To find the smallest value of y for x greater than or equal to 0, we need to find the minimum value of the expression.
1. First Step:
Simplify the expression:
y = (3x² + 6x + 6) / 2(x + 1)
y = (3x² + 6x + 6) / 2x + 2
2. Second Step:
To find the minimum value, we need to find the derivative of y with respect to x and set it equal to 0.
dy/dx = (6x + 6) / 2(x + 1) - (3x² + 6x + 6) / (2(x + 1)²) = 0
3. Third Step:
Solve for x by equating the derivative to 0 and find the critical points.
4. Fourth Step:
After finding the critical points, determine which one corresponds to the minimum value by using the second derivative test.
5. Fifth Step:
Once the minimum value is found, substitute the value of x back into the expression to find the smallest value of y.
By following these steps, you can find the smallest value of the given expression for x greater than or equal to 0.
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For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)?
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For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)?.
For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For x is greater than equal to 0, the smallest value of expression y=(3x²+6x+6)/2(x+1)?.
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