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Calculus
Practice Quiz 341

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1.  Jessica heats a circular hot plate so that the radius increases at a rate of 0.02 cm/sec.  At what rate is the area of the hot plate increasing when the radius is 100 cm.?
2.314
12.57
4		 2.  Bryant blows up a spherical balloon at a rate of 100 cc/sec.  At what rate is the radius of the balloon increasing when the diameter is 18 cm.?
.224
.884
.098
3.  Erin is standing 30km from the tracks of an approaching train.  The train is traveling 90 km/h.
How fast is the distance between the train and Erin decreasing when the train is 50km away?
77.17
35.16
110		 4.  Grant is draining a cylindrical tank that has a radius of 4m.  How fast does the water level drop when the water is drained at a rate of 3L/sec.?
-238.73
110.11
-59.68

Use this graph for questions 5 and 6:

calc3411.jpg
5.  At which point(s) are the first and second derivative of f both negative?
A and O
R
O		 6.  At which point(s) on f is the first derivative negative and the second derivative positive?
A and O
R
O
7. A root of y = x4 - 2x3 - x2 - 2x + 2
using Newton's Method is:
 .63012
.66667
.60110		 8. Identify all critical points for
f(x) = x3 + x2 - 8x + 5.
9. At what points, if any, does the graph of f(x) have a local maximum, local minimum or point of inflection
if dy/dx = 3x2 + 2x - 8.
Find the general antiderivative.
10. x:
 1/2 x2 + c
2x2 + c
x2 + c		 11. 9:
 9/2 x2 + c
9x2 + c
9x + c
12. x (5/2):
 2/7 x (7/2) + c
5/2 x (3/2) + c
2/7 x (7/2) 		13. 3x5 + 14cos(x/5):
 1/3 x 6 + 14 sin( x/5 ) + c
1/2 x 6 + 70 sin( x/5 ) + c
1/2 x 6 + 14 sin( x/5 ) + c
14. Solve this initial value problem for y = 1 when x = 2:
dy/dx = ( x + (1/x2) )
 y = ( x2/2 ) - (1/x) - (1/2)
y = ( x2/2 ) - (1/x) + c
y = ( x2 ) - (1/x) - (1/2)
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