# Exam Exam

1.- The extrema of the function y = x4- 3x3+ x2 are

 a) maxima x = 0 and 2, minimum x = 1/4 b) minima x = 0 and 2, maximum x = 1/4 c) maximum x = 0 and minimum x = 4 d) it has no extrema

2.- The function y = x·lnx is increasing in the interval:

 a) (0,1/e) b) (1/e,∞) c) (0,1) d) (1,∞)

3.- The extremum of the function y = x·lnx is:

 a) maximum x = 1 b) minimum x = 1 c) maximum x = 1/e d) minimum x = 1/e

4.- Which is the inflection point of the function ?

 a) x =1 b) x = 0 c) x = -1 d) x = -2

5.- The interval in which the function is concave up is:

 a) (-∞,-1)U(0,1) b) (-∞,-2)U(1,∞) c) (-2,1) d) (-1,0)U(1,∞)

6.- The graph of the function f(x) = -x3 - 3x2 + 1 is:

 a) b) c) d) None of them

7.- Determine the value of a,b,c,d to make the function f(x) = ax3 + bx2 + cx + d have a maximum at (0, 4) and a minimum at (2, 0)

 a) a = 1; b = -3; c = 0; d = 4 b) a = 1; b = 3; c = 0; d = 2 c) a = -1; b = 5; c = 1; d = 4 d) a = 2; b = 1; c = 1; d = 4

8.- Let the function f(x) = ax2 + bx + c. Find the values of a,b,c to make the graph of the function pass through (0,4) and the straight line y - 3 = -4(x - 1) be the tangent line of the graph in point of abscissa x = 1.

 a) a = -3; b = -2; c = 4 b) a = 2; b = -1; c = 0 c) a = 3; b = 2; c = 4 d) a = -3; b = 2; c = 4

9.- Consider a rectangle of perimeter 12 m. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume?

 a) r = 3 m and h = 3 m b) r = 1 m and h = 5 m c) r = 4 m and h = 2 m d) None of them

10.- Find the point (x,y) on the graph of y = √x nearest to the point (4,0).

 a) (0,0) b) (7/2,√14/2) c) (4,2) d) (2,√2)