1. 1) The graph of y = 3x4 - 16x3 +24x2 + 48 is concave down for
(A) x < 0
(B) x > 0
(C) x < or x > -2/3
(D) x < 2/3 or x > 2
(E) 2/3 < x < 2

2. 2) The graph of y = 3x3 - 2x2 +6x - 2 is decreasing for which interval(s)?
(B) (2/9 , )
(C) [ 0 , 2/9 ]
(D) ( -  , )
(E) None of the above

3. 3) The function f is continuous on the closed interval [0,2]
3) The function f is continuous on the closed interval [0,2]. It is given that f(0) = -1 and f(2) = 2. If f '(x)>0 for all x on [0,2] and f '' (x)<0 for all x on (0,2), then f(1) could be
(A) 0
(B) 1/2
(C) 1
(D) 2
(E) 5/2

4. 4) The water level in a cylindrical barrel is falling at a rate of one inch per minute. If the radius of the barrel is ten inches, what is the rate that water is leaving the barrel(in cubic inches per minute) when the volume is 500 cubic inches?
(A) 1
(B) 
(C) 100 
(D) 200  (E) 300 

5. 5) Let f be a function defined for all real numbers x
5) Let f be a function defined for all real numbers x. If f '(x) = , then f is decreasing on the interval
(A) ( -  , 2 )
(B) ( -  , )
(C) ( -2 , 4 )
(D) ( - 2 , )
(E) ( 2 , )
4 - x2
x - 2

6. 6) Determine the maximum value of f(x) = on [ -1, 1].
(B) -1
(C) 0
(D) 3/5
(E) 1
x2 + 4
x2 - 4

7. 7) let f be a differentiable function over [0,10] such that f(0) = 0 and f(10) = 3. If there are exactly two solutions to f(x) = 4 over (0,10), then which of these statements must be true?
(A) f ' (c) = 0 for some c on (0,10)
(B) f has a local maximum at x = 5
(C) f '' (c) = 0 for some c on (0,10)
(D) 0 is the absolute minimum of f.
(E) f is strictly monotonic.

8. The graph of the derivative of f is shown in the figure at right
The graph of the derivative of f is shown in the figure at right. Which of the following could be the graph of f ? x y 2
- 2
y = f ' (x) x y 2
- 2 x y 2
- 2
(A) x y 2
- 2
(B)
(C) x y 2
- 2 x y 2
- 2
(E)
(D)