Secondary-Storage
January 27, 2024Operating-Systems
January 27, 2024GATE 1987
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Question 34
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If f(xi) ⋅ f(xi+1) < 0 then
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There must be a root of f(x) between xi and xi+1.
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There need not be a root of f(x) between xi and xi+1.
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There fourth derivative of f(x) with respect to x vanishes at xi.
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The fourth derivative of f(x) with respect to x vanishes at xi+1.
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Question 34 Explanation:
As f(xi) ⋅ f(xi+1) < 0
means one of them is positive and one of them is negative, as their multiplication is negative.
So, when you draw the graph for f(x) where xi ≤ x ≤ xi+1.
Definitely f(x) will cut the x-axis. So there will definitely be a root of f(x) between xi and xi+1.
means one of them is positive and one of them is negative, as their multiplication is negative.
So, when you draw the graph for f(x) where xi ≤ x ≤ xi+1.
Definitely f(x) will cut the x-axis. So there will definitely be a root of f(x) between xi and xi+1.
Correct Answer: A
Question 34 Explanation:
As f(xi) ⋅ f(xi+1) < 0
means one of them is positive and one of them is negative, as their multiplication is negative.
So, when you draw the graph for f(x) where xi ≤ x ≤ xi+1.
Definitely f(x) will cut the x-axis. So there will definitely be a root of f(x) between xi and xi+1.
means one of them is positive and one of them is negative, as their multiplication is negative.
So, when you draw the graph for f(x) where xi ≤ x ≤ xi+1.
Definitely f(x) will cut the x-axis. So there will definitely be a root of f(x) between xi and xi+1.