Question

Let f be a function defined on an interval I and there exists a point “c” in I such that f(c) $\le$ f(x) for all x $\in$ I , then

• A. The number f(c) is called the global maximum of f(x) in I
• B. The number f(c) is called the global minimum of f(x) in I
• C. Global maximum occurs at x = c
• D. Global minimum occurs at x = c

Answer 1

Answer: (B), (D)

The correct options are
B

The number f(c) is called the global minimum of f(x) in I

D

Global minimum occurs at x = c

To answer this question we have to understand the concept of global minimum and the difference between global minimum and local minimum. Unlike local minimum where a point has lower output than other local points (neighborhood) global minimum is always discussed in an interval. If there is a point in the interval which has the lowest output compared to all other values in that interval then that point is said to be a global minimum and the value or output is called global minimum.