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**Kat-M** If $\displaystyle \{x_n\}$and$\displaystyle \{y_n\}$ are sequences converging to the same point $\displaystyle x_0$ such that $\displaystyle x_n$$\displaystyle <$$\displaystyle x_0$$\displaystyle <$$\displaystyle y_n$ $\displaystyle \vee$$\displaystyle n$, and if $\displaystyle f$is differentiable funtion whose derivative is continuous at $\displaystyle x_0$ and which satisfies the condition that $\displaystyle f(x_n)=f(y_n)$ $\displaystyle \vee$$\displaystyle n$, show that $\displaystyle f'(x_0)=0$.