The expression (f(2+h)-f(2))/h for the function f(x) = 5x - 6 simplifies to 5, which represents the constant slope of the linear function.
Step 1: We Calculate f(2 + h) and f(2):
f(2 + h) = 5(2 + h) - 6 = 10 + 5h - 6
f(2) = 5(2) - 6 = 4
Step 2: We Calculate the difference:
f(2 + h) - f(2) = (10 + 5h - 6) - 4 = 5h
Step 3: We Calculate the quotient by dividing by h:
(f(2 + h) - f(2)) / h = 5h / h = 5
Therefore, the difference quotient of f(x) = 5x - 6 at x = 2 with step size h is 5.