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You are not logged in. #1 20110929 21:45:33
Interesting maximum problemHi; 2) Enter into the input bar f(x) = 2*x^2  4*x and press enter. 3) Enter into the input bar g(x) = x+2 and press enter. 4) Create and label 3 points O(0,0), C(1,2), D(2,0). 5) Pick a point that is on the left of C and place it on the parabola. Label it B. 6) Now drop a perpendicular line from B to the x axis. 7) Find the intersection point between this perpendicular line from B to the line x+2. Call this point of intersection A. ( use the intersection tool ). 8) Use the distance tool to measure the distance from B to A. It will appear in the algebra pane as distanceBA = something. 9) Set rounding to 10 digits. 10) use the move tool to slide point B along the parabola. See how close you can come to 1.125, I got 1.1249967. That is the maximum length of BA. 11) Go into the algebra pane and find x = 1.24941724. That is the x coordinate you seek. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 