STATEMENT OF PROBLEM

Part A

Find the necessary vertical shift, h, of f(x) = -x^2 to x^2 + h so that the area bounded above by the new function and below by the x-axis which lies between the points of intersection of the function with the x-axis is equal to 2.

Part B

Same as part A, but make the area equal to 4. Can you see the pattern to set the area equal to any positive number n?

Part C

The area bounded above by y = f(x) = x^3 - 4x^2 - x + 4, bounded below by the x-axis, and between the two roots x = -1 and x = 1 of f(x) = 0 is 5.3333. If the value of the constant is increased by a small amount, the area enclosed (from x = -1 and x = 1 ) by that portion of the curve will increase. If the value of the constant is decreased, the area will become smaller. By what value must the constant be changed to enclose an area of 4 units by that portion of the curve?