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

Create a free account to view solution

View Solution Free
Topic: Set, Relation and Function·Practice all Set, Relation and Function questions

More Set, Relation and Function Questions

If f is a real-valued differentiable function satisfying |f(x) – f(y)| ≤ (x - y)2, x, y ∈ R and f(0) = 0, ...Let the relation R on the set $M = \{ 1,2,3,\ldots\ldots.16\}$ be given by$R = \{(x,y):4y = 5x - 3,x,y \in M\}$.Then the...In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y) | x, y ∈ A and x < y}. Then R is -...Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to...Let f(x) be a differentiable function on interval (0, ∞) such that f(1) = and then f(2) has value equal to...