Question

# A differentiable function f(x) is strictly increasing ∀xϵR, then -

A
f(x)>0xϵR
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B
f(x)0xϵR, provided it vanishes at finite number of points.
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C
f(x)0xϵR provided it vanishes at discrete points though the number of these discrete points may not be finite.
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D
f(x)0xϵR provided it vanishes at discrete points and the number of these of these discrete points must be infinite.
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Solution

## The correct option is B f′(x)≥0∀xϵR provided it vanishes at discrete points though the number of these discrete points may not be finite.For f(x) to be strictly increasing, the slope of y=f(x) at any real x should be greater than 0.That is f′(x)>0But it vanishes at discrete points though the number of these discrete points may not be finite.Hence answer is C.

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