# Exam Exam

1.- The abscissa in which the slope of the tangent line to the graph of f(x) = ex + 1 is e2, is:

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

2.- Decide which of these sentences is true:

 a) All the continuous functions are derivable ones b) Only some derivable functions are continuous functions c) A derivable function may not be continuous d) All the derivable functions are continuous ones

3.- f(x) = x2 +ex → f'(x) =

 a) x + ex b) x - ex c) 2x + ex d) None of them

4.   If f(x) = 3x4 - 5x + 2, then f'(1) equals:

 a) 6 b) 7 c) 0 d) -1

5.- f(x) = x2ex → f'(x) =

 a) xex + x2ex b) ex(x2 + 2x) c) ex (x+ 2x) d) None of them

6.   f(x) = sin3x2 → f'(x) =

 a) 6x·cos3x2 b) cos3x2 c) 2cos3x2 d) None of them

7.  If f(x) = x4 - 5x + 2, then fVII(5) =

 a) 1 b) 0 c) -1 d) 5

8.   If f(x) = x·ex, then f'''(0) =

 a) 1 b) 2 c) 3 d) 0

9.- The equation of the tangent line to the curve x2 + y2 -4xy = 1 at the point (1,4) is

 a) y - 4 = 1/2(x - 1) b) y - 4 = -1/2(x - 1) c) y - 4 = 7/2(x - 1) d) y - 1 = 7/2(x - 4)

10.- Find the value of a and b to do the function continuous and derivable in R

 a) a = 0; b = -1 b) a = 1; b =0 c) a = -1; b = 0 d) None of them