,
find the first derivative using the definition of a derivative. (the limit
process) [5 pts]Wetzel Summer 2006
Math 140
Test #2
Name:_______________________
1.) Given the function, f(x) =
,
find the first derivative using the definition of a derivative. (the limit
process) [5 pts]
2.) Find the slope of the tangent line to the graph of the function,
g(x) = 
at
the point (-1, -9). [5 pts]
Find dy/dx. [5 pts. Each]
3.) 
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4.) 
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5.) 
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6.) 
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7.) 
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8.)
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9.) 
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10.) 
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11.) 
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12.) 
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13.) 
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14.) 
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15.) 
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16.) 
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17.) Find the second derivative of the function, f(x) = 4sin x.
f ”(x) = _________________
18.) A model rocket is launched in the air from the
ground. Its height t seconds after it is launched will be
(neglecting
air resistance).
a.) Find the velocity function. [2 pts]
b.) Find velocity of the rocket 15 seconds after the launch. [3 pts]
19.) The volume of a sphere is increasing at a rate of 18
cubic inches per minute when the radius of the sphere is 3 inches. At what rate
is the length of the radius changing? [5 pts] V =
SHOW
WORK
20.) A baseball diamond has the shape of a square with sides 90 feet long. A player is running from second to third at a speed of 28 feet per second. At what rate is the player’s distance from home plate changing when he is 30 feet from third base? SHOW WORK [5 pts]
BONUS:
The included angle of the two sides of constant equal
length s of an isosceles triangle is θ. Show that the area of the triangle is
given by 
.
SHOW WORK [5 pts]