If f be a function defined on an interval I and there exists a point -a- in I such that f a - f x for all x - I- thenA- The number fa is called the global maximum of fx in IB- The number f a is called the global minimum of f x in IC- Global maximum occurs at x - aD- Global minimum occurs at x - a

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Question

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

The number f(a) is called the global maximum of f(x) in I

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

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Global maximum occurs at x = a

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Global minimum occurs at x = a

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Solution

The correct options are
A
The number f(a) is called the global maximum of f(x) in I

C
Global maximum occurs at x = a

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

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If f be a function defined on an interval I and there exists a point “a” in I such that f(a) ≥ f(x) for all x ∈ I , then

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