Consider the cubic function f :R→ R , ƒ (x)=(x-a)' (x-b) where a and b are real constants, and a +b а. Find f'(x) in terms of a and b, and state the coordinates of the maximum M and the minimum turning point N on the graph of y= f(xr). b. For what values of x is the graph of y = f(x) strictly increasing. c. Let P be the midpoint of the line joining the points M and N, show that the coordinate 2a+b 2(a-b) of the point P is given by P 3 and that the point P lies on the 27 graph of y = f(x).

An environmental engineer wants to evaluate three different methods for disposing of nonhazardous chemical waste: land application, fluidized-bed incineration, and private disposal contract. Use the estimates below to help her determine which has the least cost at /= 15.00% per year on the basis of an annual worth evaluation. First Cost AOC per Year Salvage Value Life Land $-145000 $-86000 $23000 4 years Incineration $-760000 $-70000 $260000 6 years Contract O $-132000 O 2 years

2. Find the level curve of the function f(x, y) = √y + x²-1 at the point (1, 1). Express the curve as an equation and draw it.