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
5.- f(x) = x2ex → f'(x) =
a) xex + x2ex
b) ex(x2 + 2x)
c) ex (x+ 2x)
6. f(x) = sin3x2 → f'(x) =
a) 6x·cos3x2
b) cos3x2
c) 2cos3x2
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) =
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.- f(x) = (lnx)x → f'(x) =
a) x·(lnx)x-1
b) ln(lnx)·(lnx)x
c) (ln(lnx)+1/lnx)·(lnx)x
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