JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f

be any function defined on

R

and let it satisfy the condition

\left| {f(x) - f(y)\left| {{\mkern 1mu} \le {\mkern 1mu} } \right|{{\left( {x - y} \right)}^2}} \right|,{\mkern 1mu} {\mkern 1mu} \forall \;x,y \in R

f(0) = 1

, then

View answer and explanation

Correct option: D

f(x) > 0,\,\,\forall x \in R

Option D is correct. Given the condition on

f(x)

, it can be shown that

f(x)

is a constant function, and since

f(0) = 1

f(x) = 1

for all

x

, thus

f(x) > 0

for all

x \in R

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