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## Sample Document Text

MTH 121 - Summer - 2005
Essex County College - Division of Mathematics
Test # 11 - Created May 31, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers. Justify your answers alge-
braically whenever possible. You have at most 110 minutes2 to take this 100 point exam. No
cellular phones allowed.
1. For what values of x does the graph of f (x) = x + 2sinx have a horizontal tangent? 9 points
Solution: Take the derivative, set it equal to zero and solve for x.
fprime(x) = 1 + 2cosx
0 = 1 + 2cosx
?12 = cosx
The solution is:
x = 2pi3 + 2pik or x = 4pi3 + 2pik where k ? Z .
2. Find fprime(a) using the definition. 9 points
f (z) = 2z + 1z + 3
Solution: You must use the definition to get credit.
fprime(a) = lim
h?0
f (a + h)?f (a)
h
= lim
h?0
2a + 2h + 1
a + h + 3 ?
2a + 1
a + 3
h
= lim
h?0
(2a + 2h + 1)(a + 3)?(2a + 1)(a + h + 3)
h(a + h + 3)(a + 3)
= lim
h?0
5h
h(a + h + 3)(a + 3) =
5
(a + 3)2
1This document was prepared by Ron Bannon using LATEX...

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