For the function ,

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For the function f(x)=xcos⁡1x,x≥1f(x) = x \cos \frac{1}{x}, x \ge 1 , (1) for atleast one xx in the interval [1,∞)[1, \infty) , f(x+2)−f(x)<2f(x+2) - f(x) < 2 (2) lim⁡x→∞f′(x)=1\lim_{x \to \infty} f'(x) = 1 (3) for all xx in the interval [1,∞)[1, \infty) , f(x+2)−f(x)>2f(x+2) - f(x) > 2 (4) f′(x)f'(x) is strictly decreasing in the interval [1,∞)[1, \infty)

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