1.- The extrema of the function y = x^{4}- 3x^{3}+ x^{2} 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) = -x^{3} - 3x^{2} + 1 is:

a)

b)

c)

d) None of them

7.- Determine the value of a,b,c,d to make the function f(x) = ax^{3} + bx^{2} + 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) = ax^{2} + 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

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)

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