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The real number x when added to its inverse gives the minimum value of the sum at x equal to [2003]
- a)–2
- b)2
- c)1
- d)–1
Correct answer is option 'C'. Can you explain this answer?
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The real number x when added to its inverse gives the minimum value of...
or 
For max. or min., 
= 2(+ve minima) ∴x = 1Most Upvoted Answer
The real number x when added to its inverse gives the minimum value of...
To find the real number x that minimizes the sum x + 1/x, we can use calculus.
Let f(x) = x + 1/x.
To find the minimum, we need to find the critical points of f(x). We do this by finding where the derivative of f(x) equals zero.
f'(x) = 1 - 1/x^2
Setting f'(x) equal to zero, we get:
1 - 1/x^2 = 0
Simplifying, we have:
1/x^2 = 1
Taking the square root of both sides, we get:
1/x = 1
Multiplying both sides by x, we have:
1 = x
So the critical point is x = 1.
To determine if this critical point is a minimum, we can use the second derivative test. Taking the derivative of f'(x), we get:
f''(x) = 2/x^3
Since the second derivative is positive for all x ≠ 0, the critical point x = 1 is a minimum.
Therefore, the real number x that minimizes the sum x + 1/x is x = 1.
Let f(x) = x + 1/x.
To find the minimum, we need to find the critical points of f(x). We do this by finding where the derivative of f(x) equals zero.
f'(x) = 1 - 1/x^2
Setting f'(x) equal to zero, we get:
1 - 1/x^2 = 0
Simplifying, we have:
1/x^2 = 1
Taking the square root of both sides, we get:
1/x = 1
Multiplying both sides by x, we have:
1 = x
So the critical point is x = 1.
To determine if this critical point is a minimum, we can use the second derivative test. Taking the derivative of f'(x), we get:
f''(x) = 2/x^3
Since the second derivative is positive for all x ≠ 0, the critical point x = 1 is a minimum.
Therefore, the real number x that minimizes the sum x + 1/x is x = 1.
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The real number x when added to its inverse gives the minimum value of the sum at x equal to [2003]a)–2b)2c)1d)–1Correct answer is option 'C'. Can you explain this answer?
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The real number x when added to its inverse gives the minimum value of the sum at x equal to [2003]a)–2b)2c)1d)–1Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The real number x when added to its inverse gives the minimum value of the sum at x equal to [2003]a)–2b)2c)1d)–1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The real number x when added to its inverse gives the minimum value of the sum at x equal to [2003]a)–2b)2c)1d)–1Correct answer is option 'C'. Can you explain this answer?.
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