Question

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

• A. f(b-h) > f(b)
• B. f(b-h) < f(b)
• C. f(b-h) ≥ f(b)
• D. f(b-h) ≤ f(b)

Answer 1

The correct option is A

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 function is defined to check the local minimum. Here function is defined only on the left hand side of “b”. So for “b” to be a local minimum f(b-h) > f(b).

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