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If f(x) has a maximum or a minimum at a point x0 inside the interval, then f '(x0) equals :
Correct answer is '0'. Can you explain this answer?
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Iff(x)has a maximum or a minimum at a pointx0inside the interval, then...
It is necessary that at the point of maxima or minima of a function, say f, f ' will become zero.
The correct answer is: 0
Most Upvoted Answer
Iff(x)has a maximum or a minimum at a pointx0inside the interval, then...
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Explanation:
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Understanding the concept:
When a function has a maximum or a minimum at a point x0, it means that the derivative of the function at that point is equal to zero. This is because at a maximum or minimum point, the function changes direction, and the slope of the function becomes zero.
Relationship between maximum/minimum and derivative:
At a maximum or minimum point x0, the derivative of the function f(x) is equal to zero. This is a critical point because it indicates a change in the behavior of the function at that point.
Value of the function at the maximum/minimum point:
Since the derivative of the function at the maximum or minimum point x0 is zero, the value of the function at that point, f(x0), is determined by the behavior of the function around that point, not by the derivative itself.
Conclusion:
Therefore, when a function has a maximum or minimum at a point x0 inside the interval, the value of the function at that point, f(x0), can be any real number, including zero. This is because the value of the function at a maximum or minimum point is determined by the behavior of the function around that point, not by the derivative itself.
Explanation:
- - -
Understanding the concept:
When a function has a maximum or a minimum at a point x0, it means that the derivative of the function at that point is equal to zero. This is because at a maximum or minimum point, the function changes direction, and the slope of the function becomes zero.
Relationship between maximum/minimum and derivative:
At a maximum or minimum point x0, the derivative of the function f(x) is equal to zero. This is a critical point because it indicates a change in the behavior of the function at that point.
Value of the function at the maximum/minimum point:
Since the derivative of the function at the maximum or minimum point x0 is zero, the value of the function at that point, f(x0), is determined by the behavior of the function around that point, not by the derivative itself.
Conclusion:
Therefore, when a function has a maximum or minimum at a point x0 inside the interval, the value of the function at that point, f(x0), can be any real number, including zero. This is because the value of the function at a maximum or minimum point is determined by the behavior of the function around that point, not by the derivative itself.
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Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer?
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Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer?.
Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Iff(x)has a maximum or a minimum at a pointx0inside the interval, thenf '(x0)equals :Correct answer is '0'. Can you explain this answer?.
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