U ujgilani Oct 2012 17 0 london Oct 27, 2012 #1 any hints to solve the following !! Show that \(\displaystyle f(x)\) is the derivative of\(\displaystyle f(.)\) at\(\displaystyle x\) if and only if \(\displaystyle lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0 \) Last edited: Oct 27, 2012

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