Let a differentiable function f:RtoR be such that for all x and y in R 2|f(x)-f(y)|le|x-y| and f^(')(x)ge(1)/(2). So then the number of points of intersection of the graph y=f(x) with

Let a differentiable function f:RtoR be such that for all x and y in R

1.	Let a differentiable function f:RtoR be such that for all x and y in R 2\|f(x)-f(y)\|le\|x-y\| and f^(')(x)ge(1)/(2). So then the number of points of intersection of the graph y=f(x) with
Answer» the line `y=x` is one. the curve `y=-x^(3)` is one. the curve `2y=\|x\|` is three. the curve `y^(2)=-x` may be more than one. Solution :We have `2\|f(x)-f(y)\|lt\|x-y\|` `implies\|(f(x)-f(y))/(x-y)\|lt(1)/(2)implies\|f^(')(x)\|lt(1)/(2)` but `f^(')(x)GE(1)/(2)`. So `f^(')(x)=(1)/(2)` so the curve is`y=(x)/(2)+c`

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Let a differentiable function f:RtoR be such that for all x and y in R 2|f(x)-f(y)|le|x-y| and f^(')(x)ge(1)/(2). So then the number of points of intersection of the graph y=f(x) with

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