If `f` is a real-valued differentiable function satisfying `|f(x)-f(y)|leq(x-y)^2, x,y in R and f(0)=0`, then `f(1)` equals:

Options

A. 1
B. 2
C. 0
D. `-1`

Answer

C

Explanation

Since, `|f(x)-f(y)|le(x-y)^(2)`
`implies underset(xtoy)(lim)(|f(x)-f(y)|)/(|x-y|)leunderset(xtoy)(lim)|x-y|`
`implies|f'(y)|le0`
`impliesf'(y)=0`
`impliesf(y)=`constant
`impliesf(y)=0`
`impliesf(1)=0[becausef(0)=0," given"]`