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Question
A function f(x) will have a local maximum at x = c if
[ h is positive and tends to zero]
A function f(x) will have a local maximum at x = c if
[ h is positive and tends to zero]
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Solution
The correct option is B f(c-h) < f(c) & f(c) > f(c+h)
From the definition of local maximum, we know that it is a point which has higher output compared to its neighborhood which is from both the sides left and right. In other words f(x) will have a local maximum at x = c if f(c) > f(c-h) and f(c) > f(c+h) where h is an infinitesimal positive number. So option B is correct. Option A is the condition for monotonically increasing function.
f(c-h) < f(c) & f(c) > f(c+h)
From the definition of local maximum, we know that it is a point which has higher output compared to its neighborhood which is from both the sides left and right. In other words f(x) will have a local maximum at x = c if f(c) > f(c-h) and f(c) > f(c+h) where h is an infinitesimal positive number. So option B is correct. Option A is the condition for monotonically increasing function.
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