Let f:R→Rbe a differentiable function for all values of x and has the property that f (x) and f '(x) have opposite signs for all values of x. Then,

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f (x) is an increasing function

f (x) is a decreasing function

f2(x) is a decreasing function

|f(x)| is an increasing function

answer is C.

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Detailed Solution

f(x)f′(x)<0∀x∈R or 12ddxf2(x)<0 or ddxf2(x)<0Thus,f2(x) is a decreasing function.

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