Math121Quiz3Sols

Math121Quiz3Sols - QUIZ #3 (SECTIONS 3.1, 3.2, 3.3, 3.6)...

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QUIZ #3 (SECTIONS 3.1, 3.2, 3.3, 3.6) SOLUTIONS MATH 121 – FALL 2003 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% 1) Sketch the graph of fx x x () =- + 43 . You must: • Find and label all points at critical numbers and inflection points (if any). • Classify all points at critical numbers as relative maximum points, relative minimum points, or neither. • Find the y -intercept. • Have your graph correctly show where f is increasing / decreasing, and where f is concave up / concave down. • Show all steps, as we have done in class. (30 points) Step 1 : Domain = R . Step 2 : Find ¢ f and critical numbers (CNs). x fx x x xx + ¢ 32 2 41 2 This is never DNE. It equals 0 at x = 0 and x = 3, which are in the domain of f . The CNs are 0 and 3. Step 3 : Do a sign diagram for ¢ f and classify the points at the CNs. Test x = - 1 0 Test x = 1 3 Test x = 4 ¢ f sign - - + f Classify Points at CNs (Using 1 st DT.) Neither R.Max. nor R.Min. Pt. R.Min. Pt. Plug into to get y 00 , f 0,3 33 , f 3, 24 -
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¢ () =() () - ¢ - ()=+ () + () - () =- ¢()=+ ¢ () =+ fx x x f f f 43 1 1 4 2 Step 4 : Skeleton graph for f ; y -intercept y -intercept = f 03 () = , the constant term from the rule. (We already knew that 03 , was on the graph of f. ) Step 5 : Find ¢¢ f and possible inflection numbers (PINs). ¢ =- x x x x xx 41 2 12 24 12 2 32 2 f is never DNE. It equals 0 at x = 0 and x = 2, which are in the domain of f . The PINs are 0 and 2. Step 6 : Do a sign diagram for f and find inflection points (IPs). Test x = - 1 0 Test x = 1 2 Test x = 3 f sign + - + f graph CU » CD « CU » Inflection Points (IPs)? Yes, IP Yes, IP Plug into to get y 00 , f 0,3 22 , f 2, 13 -
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¢¢ () = () ( ) - - =+ () - ()=+ ¢¢() () + ()=- fx xx f f f 12 2 1 1 3 Step 7 : Sketch the graph of f . 2) Find all critical numbers of = + 1 6 2 . Remember to clearly box in your answer(s). (6 points) We must first find ¢ .
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This note was uploaded on 09/08/2011 for the course MATH 121 taught by Professor Staff during the Spring '11 term at Mesa CC.

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Math121Quiz3Sols - QUIZ #3 (SECTIONS 3.1, 3.2, 3.3, 3.6)...

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