If f ∈ R [a, b], consider the following statements :

(a) 'f' is continuous on [a, b]

(b) 'f' is monotonic on [a, b]

Which of the following is correct?

Question

Question

This question was previously asked in

RPSC 2nd Grade Mathematics (Held on 30th June 2017) Official Paper

Answer 1

Given:

If f ∈ R [a, b]

Concept:

Monotonicity of a function in a closed interval.

Continuity of a function in a closed interval.

Solution:

Since for any given function, it isn't true that every continuous function is monotonic in a neighborhood of every point provided in the interval.

So, if f ∈ R [a, b] is continuous then it need not be a monotonic function.

But if f ∈ R [a, b] is monotone then it will be a continuous function too.

Hence, neither (a) nor (b) is correct.

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