A. [MATH]\frac{\Delta f}{\Delta x}=\frac{f\left(\dfrac{\pi}{2}\right)-f\left(\dfrac{\pi}{4}\right)}{\dfrac{\pi}{2}-\dfrac{\pi}{4}}=\frac{1-\dfrac{1}{\sqrt{2}}}{\dfrac{\pi}{4}}=\frac{2\sqrt{2}(\sqrt{2}-1)}{\pi}[/MATH]

A. [MATH]\frac{\Delta f}{\Delta x}=\frac{f\left(\dfrac{\pi}{2}\right)-f\left(\dfrac{\pi}{4}\right)}{\dfrac{\pi}{2}-\dfrac{\pi}{4}}=\frac{1-\dfrac{1}{\sqrt{2}}}{\dfrac{\pi}{4}}=\frac{2\sqrt{2}(\sqrt{2}-1)}{\pi}[/MATH]