2. Graph the following functions: () () = { 2 + 7 < 2 2 1 2 2 2 + 7 > 2 () () = 1 + 2; () () = log( 2) + 1.

12. Find x for x = x(t) defined implicitly by ln = 1 t t x xe .

13. () Given = 2 + 2 , find (1,0); () Given ln + 2 = 2 3 , find (1,1).

14. Find the equation of the line perpendicular to the curve f (x) = x at the point P( 4, f(4) ).

15. Let ( ) 6 10 4 2 f x = x x + . Find the equation of the tangent line at x = 1, and find the values of x where the tangent line is horizontal.

16. Suppose a point is moving along the graph o f 25 2 2 x + y = . When the point is at ( 3, 4 ), its coordinate is increasing at the rate of 0.4 units per second. How fast is the y coordinate changing at that moment? (HINT: Consider both x and y as a functions of t, i.e. = (), = () ).

17. Find the extremum point of f(x)=x+x/4 on the intreval(0,infinity)

18. Suppose that at the certain factory setup cost is directly proportional to the 4 number of machines used, and operating cost is inversely proportional to the number of machines used. Show that when the total costs is minimal, the setup cost is equal to the operating cost. (Hint: Total cost = setup cost + operating cost)