Set, Relation and FunctionHard
Question
If f is a real-valued differentiable function satisfying |f(x) – f(y)| ≤ (x - y)2, x, y ∈ R and f(0) = 0, then f(1) equals
Options
A.-1
B.0
C.2
D.1
Solution
f′(x) = 
|f′(x)| =
⇒ |f′(x) ≤ 0 ⇒ f′(x) = 0 ⇒ f(x) = constant
As f(0) = 0 ⇒ f(1) = 0.
|f′(x)| =
⇒ |f′(x) ≤ 0 ⇒ f′(x) = 0 ⇒ f(x) = constant
As f(0) = 0 ⇒ f(1) = 0.
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