Given the function
\(f(x)=\dfrac{1}{4}\,2^{x}\)
The average rate between \(f(2)\) and \(f(5)\) is
\(\left.\dfrac{\Delta f}{\Delta x}\right|_{x=2\to 5}=\dfrac{f(5)-f(2)}{5-2}\\ \\ \\ =\dfrac{\frac{1}{4}\cdot 2^{5}-\frac{1}{4}\cdot 2^{2}}{5-2}\\ \\ \\ =\dfrac{\frac{1}{4}\cdot (2^{5}-2^{2})}{3}\\ \\ \\ =\dfrac{\frac{1}{4}\cdot (32-4)}{3}\\ \\ \\ =\dfrac{\frac{1}{4}\cdot (28)}{3}\\ \\ \\ =\dfrac{7}{3}\)
