Question

54. If f is real-valued differentiable function satisfying [f(x) - f)](x - y)2,x,y e R and f(0) = Q, then f(1) equals: - ​

Answer 1

Answer:

f is a real valued differential function. So,

lim

h→0

∣f(x+h)−f(x)∣≤(x+h−x)

2

⇒lim

h→0

∣f(x+h)−f(x)∣≤∣h∣

2

⇒lim

h→

h

f(x+h)−f(x)

≤0⇒f

′

(x)=0

⇒f(x) is constant function

∵f(0)=0⟹f(1)=0