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Test 1 Fall 2009: Key

# Test 1 Fall 2009: Key - Math 111 Test 1 Pledged 110 points...

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---------- Math 111 Test 1 Pledged _ 110 points fall 2009 Print Name Your signature on the line above gives your pledge that this test was done by you and represents your work. 1. Determine if the Intermediate Value Theorem applies or does not apply to the following: F(x) = x 3 _x 2 -6x [-3,4] F(c) = 0 Be clear and complete in your argument. If appropriate, find c. (12 points) (j) F (Xl i 5 COY\4-)Y"(,LOV-S eV --rljwt S l·ne. e F j 5 polj nOY'A\<A.L @ F(-3):= (-3) -= -27 - q + ,g =- -I <;? F( 4 ') = (LJ J (LJ) (1-\ J :: {P 1-{ - I {P - d Y :;: d if Q F(-3J=-\g <: <: Ih eAthn-e W ieA rA-J-dJ-O:t::t Jh ... Q 3 '2. F (C)::: C - - /.p C := 0 C LC:'C. =0 11=0 C=3 l.-) ) CvU- Cs: - 0. =-3 C 3 ==jJ< b=-J-j

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-- 2. a) State the definition of derivative. (5 points) +'(,x') = .f(X-+-6x)- -F'{X) L! 6 X 0 /j X ) '"::::- ===== b) Use the definition to find the derivative for f (x) = _1_. Show all steps clearly. (6 3-x points) I \ fl(Xl == 3-(X+'LlX) - 6X-7D - LlX I1sl'de: 3-X - [3-(X-t-6XI] I n IA rn enJ-or; /- y:- fi' (3 - (X +-t1x)) (.3-X l .6X tJ-'/0 (3-XJ -;z.. c) Give the equation of the normal line to the function in part b at x = 2. (3 points) +( ;l) = - I :::: \ ( ;1/ I') \ S (JO l(\ -C \f ') :: - \ .
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