Given f ( x ) = 1 x + 5 , find the average rate of change of f ( x ) on the interval [ 6 , 6 + h ] . Your answer will be an expression involving h .

Answer 1

f(x) = x + 5

f(6) = 6+5 = 11

f(6+h) = 6+h+5 = 11+h

f(6+h) - f(6) = 11+h - 11 = h

average rate of change = [f(6+h) - f(6)]/(6+h-6) = h/h = 1

To short circuit all the calculations, just notice that f(x)=x+5 is a linear equation with slope = 1, which has instantaneous = average rate of change = slope = 1 = the coefficient of the x term