This exercise invoves a diference quotient for an exponental

This exercise invoves a diference quotient for an exponental finction If f(x) = 2x, show that f(x + h) - f(x) 2X Simplify your answers completely at each step. /(x)= 2x, so SO fx + h) - ffx) (2X) 2h-1

Solution

Given   f(x) = 2^x

f(x + h) = 2^x+h

[f(x + h) – f(x)]/h = (2^x+h - 2^x)/h = (2^x2^h - 2^x)/h

                = 2^x[2^h - 1]/h