Consider the following.

f(x) = 8x (square root of (x − x^2))

(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.

well, f(x) is only defined on 0 <= x <= 1

Visit

http://rechneronline.de/function-graphs/

and enter 8x*sqr(x-x^2) for your function. Set the range of y to be 2.5 to 3 and the peak will be quite clear

To find the absolute maximum and minimum values of a function, we can follow these steps:

1. First, find the critical points of the function by taking the derivative and solving for when it equals zero or is undefined.
2. Evaluate the function at the critical points and endpoints of the interval of interest.
3. Compare the values obtained in step 2 to determine the absolute maximum and minimum.

In this case, we need to use a graph to visualize the function and identify the interval of interest. Let's plot the graph of the given function f(x) = 8x * sqrt(x - x^2).

To do this, we can use a graphing calculator or software like Desmos.com or WolframAlpha. The graph will help us identify the interval over which we need to find the maximum and minimum values.

After plotting the graph, we can examine the shape of the function and identify any local maxima or minima. We can then use the identified points to determine the absolute maximum and minimum.

Please note that without the specific interval, it is challenging to determine the exact absolute maximum and minimum for a given function. If you provide the interval, we can proceed further to find the required values.