Question

Evaluate the difference quotient for the given function. Simplify your answer.

f(x) = 3(3x - x²), f(3h) - f(3)/h

Answer 1

To evaluate the difference quotient for the given function f(x) = 3(3x - x²), substitute 3h and 3 into the function, subtract the results, and divide by h to get the simplified difference quotient.

Step-by-step explanation:

To evaluate the difference quotient for the given function f(x) = 3(3x - x²), we need to find f(3h) and f(3) and then subtract them, and divide the result by h.

First, substitute 3h into the function: f(3h) = 3(3(3h) - (3h)²) = 3(9h - 9h²).

Next, substitute 3 into the function: f(3) = 3(3(3) - (3)²) = 3(9 - 9) = 0.

Now, we can calculate the difference quotient: (f(3h) - f(3))/h = (3(9h - 9h²) - 0)/h = (27h - 27h²)/h = 27 - 27h.