Math121SampleQuiz3Sols

Math121SampleQuiz3Sols - QUIZ #3 (SAMPLE SOLUTIONS) USE A...

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QUIZ #3 (SAMPLE SOLUTIONS) USE A SCIENTIFIC CALCULATOR! 1) For parts a) and b), sketch the graph of f . You must: • Find and label all critical points and inflection points (if any). • Classify all critical points 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. (44 points total) a) fx x x x () =+-+ 292 4 20 32 . (26 points) Step 1 : Domain = R . Step 2 : Find ¢ f and critical numbers (CNs). x x x fx x x xx =+- + ¢ =+- =+ - - 4 20 61 8 2 4 63 4 64 1 2 2 This is never DNE, but it equals 0 at x =- 4 and x = 1, which are in the domain of f . The CNs are - 4 and 1.
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Step 3 : Do a sign diagram for ¢ f and classify critical points (CPs). Test x = - 5 - 4 Test x = 0 1 Test x = 2 ¢ f sign + - + f Classify CPs R.Max. Pt. R.Min. Pt. Plug into fx () to get y -- 44 , f - 4,132 11 , f 1,7 ¢ () =() + - ¢ - ()=+ () - () =+ ¢ () + () =- ¢ x x f f f 641 5 0 2 Step 4 : Skeleton graph for f ; y -intercept y -intercept = f 02 0 () = , the constant term from the rule. Step 5 : Find ¢¢ f and possible inflection numbers (PINs). ¢ =+- =+ fx x x x x 61 8 2 4 12 18 62 3 2 Note: 23 0 3 2 15 x x x += =- - or . f is never DNE, but it equals 0 at x . , which is in the domain of f . The sole PIN is - 1.5.
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Step 6 : Do a sign diagram for ¢¢ f and find inflection points. Test x = - 2 - 1.5 Test x = 0 f sign - + f graph CD « () CU » Inflection Points (IPs)?
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Math121SampleQuiz3Sols - QUIZ #3 (SAMPLE SOLUTIONS) USE A...

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