Show that $\displaystyle f(x)$ is the derivative of$\displaystyle f(.)$ at$\displaystyle x$ if and only if $\displaystyle lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0 $

Printable View

- Oct 27th 2012, 08:55 AMujgilaniany hints to solve the following !!
Show that $\displaystyle f(x)$ is the derivative of$\displaystyle f(.)$ at$\displaystyle x$ if and only if $\displaystyle lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0 $