Question

A function f(x) defined on [a,b] will have a local maximum at x = b if

[ h is a positive quantity tending to zero]

• A. f(b-h) > f(b)
• B. f(b-h) < f(b)
• C. f(b-h) $\ge$ f(b)
• D. f(b-h) $\le$ f(b)

Answer 1

The correct option is B

f(b-h) < f(b)

Here, point “b” is the the boundary point. We know, that if there is a boundary point then we have to consider only one side of that point where the function is defined to check the local maximum. Here function is defined only on the left hand side of “b”. So for “b” to be a local maximum f(b-h) < f(b).

Note - Even if f(b-h) is equal to f(b) then also there is no local maximum. That's why option D is incorrect.