Question

Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 1/(4x - x²), f(3h) - f(3)/h

Answer 1

To evaluate the difference quotient for the given function, f(x) = 1/(4x - x²), substitute f(3h) and f(3) into the difference quotient formula and simplify the expression.

Step-by-step explanation:

To evaluate the difference quotient for the given function, f(x) = 1/(4x - x²), we need to substitute f(3h) and f(3) into the difference quotient formula and simplify the expression. The difference quotient formula is given as: f(3h) - f(3)/h. Let's calculate it step by step.

First, substitute 3h into the function: f(3h) = 1/(4(3h) - (3h)²).

Next, substitute 3 into the function: f(3) = 1/(4(3) - (3)²).

Now, calculate the difference quotient by subtracting f(3) from f(3h) and dividing it by h: (f(3h) - f(3))/h.

Finally, simplify the expression to obtain the answer.