Set, Relation and FunctionHard

Question

Let a differentiable function f(x) be such that 3|f(x) - f(y)| ≤ 2|x - y| ∀ x, y ∈ R and f′(x) ≥ . Then the number of points of intersection of the graph of y = f(x) with

Options

A.the line y = x is one
B.the curve y = - x3 is one
C.the curve 2y = |x| is three
D.none of these

Solution

⇒ (f′(x)) =
but given f′(x) ≥ ⇒ f′(x) =
⇒  f(x) = + C

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