Question

Utiliza-se o Teste da Segunda Derivada para encontrar extremos locais. Suponha que f'' seja contínua em um intervalo aberto que contenha x=c. bold bullet Se space straight f hat apostrophe space left parenthesis straight c right parenthesis equals 0 space straight e space straight f hat apostrophe apostrophe space left parenthesis straight c right parenthesis less than 0 comma space então space straight f space tem space um space máximo space local space em space straight x equals straight c. bullet S e space f apostrophe space left parenthesis c right parenthesis equals 0 space e space f apostrophe apostrophe space left parenthesis c right parenthesis greater than 0 comma space e n t ã o space f space t e m space u m space m í n i m o space l o c a l space e m space x equals c. bullet S e space f apostrophe space left parenthesis c right parenthesis equals 0 space e space f apostrophe apostrophe space left parenthesis c right parenthesis greater than 0 comma space e n t ã o space f space t e m space u m space m í n i m o space l o c a l space e m space x equals c. bullet S e space f apostrophe space left parenthesis c right parenthesis equals 0 space e space f apostrophe apostrophe space left parenthesis c right parenthesis equals 0 comma space e n t ã o space o space t e s t e space f a l h a. spacespace space space A space f u n ç ã o space f space p o d e space t e r space m á x i m o space l o c a l comma space o u space m í n i m o space l o c a l space o u space n e n h u m space d o s space d o i s. Tendo como base o Teste da Segunda Derivada, encontre uma função cúbica f left parenthesis x right parenthesis equals a x cubed plus b x squared plus c x plus d que tenha um valor máximo local 3 em -2 e um valor mínimo local 0 em 1: Agora, assinale a alternativa correta. Escolha uma: a. f left parenthesis x right parenthesis equals 2 over 3 x cubed plus 1 third x squared plus 4 over 3 x plus 7 over 9 b. f left parenthesis x right parenthesis equals 2 over 9 x cubed plus 1 third x squared minus 4 over 3 x plus 7 over 9 c. f left parenthesis x right parenthesis equals negative 2 over 9 x cubed plus 1 third x squared plus 4 over 3 x plus 7 over 3 d. f left parenthesis x right parenthesis equals negative 2 over 9 x cubed plus 1 third x squared plus 4 over 3 x plus 7 over 9 e. f left parenthesis x right parenthesis equals 2 over 3 x cubed plus 1 over 9 x squared plus 4 over 3 x plus 7 over 9

Answer 1

     2/9x^3+1/3x^2-4/3x+7/9