1.- The abscissa in which the slope of the tangent line to the graph of f(x) = e^{x} + 1 is e^{2}, 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) = x^{2} +e^{x} → f'(x) =

a) x + e^{x}

b) x - e^{x}

c) 2x + e^{x}

d) None of them

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

a) 6

b) 7

5.- f(x) = x^{2}e^{x} → f'(x) =

a) xe^{x} + x^{2}e^{x}

b) e^{x}(x^{2} + 2x)

c) e^{x} (x+ 2x)

6. f(x) = sin3x^{2} → f'(x) =

a) 6x·cos3x^{2}

b) cos3x^{2}

c) 2cos3x^{2}

7. If f(x) = x^{4} - 5x + 2, then f^{VII}(5) =

a) 1

b) 0

c) -1

d) 5

8. If f(x) = x·e^{x}, then f'''(0) =

b) 2

c) 3

d) 0

9.- The equation of the tangent line to the curve x^{2} + y^{2} -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

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