4) What can be said about the relationship between the graph of afunction and thetangentline at a point of inflection?

5) Let S represent the daily sales of a given item. ( S(x) = items sold at day x )

What can be said about of S' and S'' for each of the following statements?

(a) The rate of change of sales is increasing.

(b) Sales are increasing at a slower rate.

(c) The rate of change of sales is constant.

(d) Sales are steady.

(e) Sales are declining, but at a slower rate.

(f) Sales have bottomed out and have started to rise.

7) Find a function of two variables f(x,y) for which D = 0, but the function has a minimum.

8) What are the advantages and disadvantages of the method of Lagrange multipliers compared with solving the equation g(x,y) =0 for y (or x), substituting that expression into f and then minimizing or maximizing f as a function of one variable.