Let $f(x)=-x^{2}+9 x$ Find the slope of the secant line on the graph of $f(x)$ for each interval: [3,3.01]

Step 1 ：Let's consider the function \(f(x)=-x^{2}+9 x\).

Step 2 ：We need to find the slope of the secant line on the graph of \(f(x)\) over the interval [3,3.01].

Step 3 ：The slope of the secant line between two points on a function is given by the difference in the y-values of the points divided by the difference in the x-values of the points. This is also known as the average rate of change of the function over the interval.

Step 4 ：We can calculate the slope as follows: Slope = \(\frac{f(3.01) - f(3)}{3.01 - 3}\).

Step 5 ：Substitute the function \(f(x)\) into the formula and calculate the result.

Step 6 ：The slope of the secant line on the graph of \(f(x)\) over the interval [3,3.01] is approximately 2.99.

Step 7 ：Final Answer: The slope of the secant line on the graph of \(f(x)\) over the interval [3,3.01] is \(\boxed{2.99}\).