Let g(t)=2t-1. Find and simplify g(t+h)-g(t)/h

Answer 1

This is the difference quotient of the function.

g(t+h) = 2(t+h)-1 = 2t+2h - 1

g(t+h) - g(t) = 2t+2h - 1 - (2t-1) = 2t + 2h - 1 - 2t + 1 = 2h

Divided by h results in a difference quotient of 2h/h = 2