First you need to determine the roots of the function, so you know what bounds to use.
use a graphing utility to graph f(x)=x^4-6x^3+11x^2-6x. then use the upper sums to approximate the area of the region in the first quadrant is bounded by f and the x axis using 4 subintervals. round your answer to three decimals
I have no idea how to do this and its due wednesday, we've never even talked about it in class
Please help!
Good. Now separate that interval into four subintervals of the same length and determine the maximum value of the function on each subinterval. Then the approximation of the area desired is . Hint: Use the first derivative of the function to determine whether the function is increasing or decreasing on each subinterval.
This is not the same as the upper sums. For the upper sums, you want the maximum value of the function on each subinterval. It turns out that f(5/4) and f(3/2) are the maximum values of the function on the intervals [1, 5/4] and [5/4, 3/2] respectively, but the other two numbers you have are not.