Final answer:
The difference quotient for the function f(x) = x² + 4 is calculated to be 2x + h after simplifying the expression obtained by applying the difference quotient formula.
Step-by-step explanation:
The difference quotient for a function f(x) is given by the formula f(x + h) - f(x) / h. For the given function f(x) = x² + 4, we will apply this formula. We calculate f(x + h) as ((x + h)² + 4). The difference quotient is then ((x + h)² + 4 - (x² + 4)) / h. Simplifying, we get ((x² + 2xh + h² + 4) - (x² + 4)) / h, which further simplifies to (2xh + h²) / h. Canceling out h from numerator and denominator gives us the final answer, 2x + h.