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NC1. If f(x)=sin2(3-x), then f ′(0)=
(A) –2cos3
(B) –2sin3cos3
(C) 6cos3
(D) 2sin3cos3
3
dy x
NC2. The solution to the differential equation
, where y(2)=3, is

dx y 2
(E) 6sin3cos3
3 4
3
3
3
3
x
( B) 3 x 4  3 15
(C ) 3 x 4  15
( D) 3 x 4  5
( E) 3 x 4  15
4
4
4
4
4
2
NC3. If g is a differentiable function such that g(x)<0 for all real numbers x and if f ′(x)=(x -4)g(x), which of
the following is true?
(A) f has a relative maximum at x=-2 and a relative minimum at x=2
(B) f has a relative minimum at x=-2 and a relative maximum at x=2
(C) f has a relative minimum at x=-2 and at x=2
(D) f has a relative maximum at x=-2 and at x=2
(E) It cannot be determined is f has any relative extrema
(ln x)3
NC4. Let F(x) be the antiderivative of
. If F(1)=0, then F(9)=
x
(A) 0.048
(B) 0.144
(C) 5.827
(D) 23.308
(E) 1,640.250
 x2
C5. Consider the graph of the function h( x)  e for 0  x  1 .
(a) Let R be the region in the first quadrant below the graph of h. Find the volume of the solid
generated when R is revolved about the y-axis..
(b) Let A(x) be the area of the shaded rectangle shown in the figure to the right. Find the x-coordinate
that maximizes A(x).
( A) 3
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