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1985BC6 - I985 EC(9 6 Let f be a function that is...

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Unformatted text preview: I985 «- EC. (9 6. Let f be a function that is defined and twice differentiable for all real numbers x and that has t following properties. 6) N3) = 2 (ii) f ’(x)‘> 0 for all x (iii) The graph of f is concave up for all x > 0 and concave down for all x < 0 Let g be the function defined by g(x) =f(x2). (3) Find 3(0). (b) Find the x-coordinates of all minimum points of g. Justify your answer. (c) Where is the graph of g concave up? Justify your answer. (d) Using the information found in parts (a), (b), and (c), sketch a possible graph of g on the as provided below. a.) $03) = {1(0) == 2 5) q'bfi =a1xw°'(x‘):, ¥’(x")>o Vx. (5.5, LL). Then: ((X)=o when )(201 CLMGL ($0070 {tor X70 =? :3 increasing {lop x70 “>040 ~For 3(40 :3. c3 deer-eas'mci4'or x40 ‘3 .'. Since %(0\ exists) (3 has an abSOlu‘l'e min at X=O OR, filba : #63): + +’ 2x: - +' X 0 . G-r-‘LPk 0" :3: Fa.” Rise. o.) 3%: MM) Home) a 4’0?) >0 Vx (b3 ca),1°”(x*)>o Vx (:93 age), x 2.0 => 3"00 >0 Vx ’. % is Concave. up eVerquher’e. co 1985 BC6 ...
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