Final answer:
The difference quotient for the function f(x) = 4x² + 3x is 8x + 4h + 3, where h is a small number.
Step-by-step explanation:
The difference quotient is used to find the average rate of change of a function over a small interval. In this case, we have the function f(x) = 4x² + 3x. To find the difference quotient, we need to evaluate (f(x+h) - f(x)) / h, where h is a small number.
Let's plug in the values into the formula and simplify:
(f(x+h) - f(x)) / h = ((4(x+h)² + 3(x+h)) - (4x² + 3x)) / h
= (4x² + 8xh + 4h² + 3x + 3h - 4x² - 3x) / h
= (8xh + 4h² + 3h) / h
= 8x + 4h + 3
So the difference quotient is 8x + 4h + 3.