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Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional part)
- a)A point of local maxima
- b)A point of local minima
- c)Neither a point of local minima nor maxima
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional p...
Explanation:
Given function is f(x) = {x}, where {*} denotes the fractional part.
The fractional part of a number is always between 0 and 1, inclusive. For example, the fractional part of 3.14 is 0.14.
To find if x = 5 is a point of local maximum or minimum, we need to look at the values of f(x) near x = 5.
Local Maximum:
A point is said to be a local maximum if there exists some interval around that point such that all the values of the function in that interval are less than or equal to the value of the function at that point.
For f(x) = {x}, there is no interval around x = 5 such that all the values of f(x) in that interval are less than or equal to the value of f(5). This is because the fractional part of any number in the interval (5, 6) is greater than the fractional part of 5.
Therefore, x = 5 is not a point of local maximum.
Local Minimum:
A point is said to be a local minimum if there exists some interval around that point such that all the values of the function in that interval are greater than or equal to the value of the function at that point.
For f(x) = {x}, there is an interval around x = 5 such that all the values of f(x) in that interval are greater than or equal to the value of f(5). This is because the fractional part of any number in the interval [5, 6) is greater than or equal to the fractional part of 5.
Therefore, x = 5 is a point of local minimum.
Conclusion:
Therefore, the correct answer is option B, x = 5 is a point of local minimum for the function f(x) = {x}.
Given function is f(x) = {x}, where {*} denotes the fractional part.
The fractional part of a number is always between 0 and 1, inclusive. For example, the fractional part of 3.14 is 0.14.
To find if x = 5 is a point of local maximum or minimum, we need to look at the values of f(x) near x = 5.
Local Maximum:
A point is said to be a local maximum if there exists some interval around that point such that all the values of the function in that interval are less than or equal to the value of the function at that point.
For f(x) = {x}, there is no interval around x = 5 such that all the values of f(x) in that interval are less than or equal to the value of f(5). This is because the fractional part of any number in the interval (5, 6) is greater than the fractional part of 5.
Therefore, x = 5 is not a point of local maximum.
Local Minimum:
A point is said to be a local minimum if there exists some interval around that point such that all the values of the function in that interval are greater than or equal to the value of the function at that point.
For f(x) = {x}, there is an interval around x = 5 such that all the values of f(x) in that interval are greater than or equal to the value of f(5). This is because the fractional part of any number in the interval [5, 6) is greater than or equal to the fractional part of 5.
Therefore, x = 5 is a point of local minimum.
Conclusion:
Therefore, the correct answer is option B, x = 5 is a point of local minimum for the function f(x) = {x}.
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Community Answer
Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional p...
At minima value of function is mininum in FIF minimum value is 0 which occurs at integer.so f(5)=f{5}=0 is minima
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Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional part)a)A point of local maximab)A point of local minimac)Neither a point of local minima nor maximad)None of theseCorrect answer is option 'B'. Can you explain this answer?
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