Let $f(x)=-x^2+9x$
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 $f(x)=-x^2+9x$.

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 $\boxed{{\displaystyle 2.99}}$.