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gma00108-lista-09 - LISTA DE EXERC ICIOS DEPARTAMENTO DE...

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GMA DEPARTAMENTO DE MATEMÁTICA APLICADA LISTA DE EXERC ´ ICIOS alculo I –A– Humberto Jos´ e Bortolossi http://www.professores.uff.br/hjbortol/ 09 Defini¸ ao de derivada, retas tangentes, taxas de varia¸ ao e derivadas laterais [01] O custo (em reais) de produzir x unidades de uma determinada mercadoria ´ e dada pela fun¸ c˜ao f ( x ) = 5000 + 10 x + 0 . 05 x 2 . (a) Encontre a taxa de varia¸ c˜ao m´ edia de f em rela¸c˜ao a x quando os n´ ıveis de produ¸ c˜ao estiverem variando: (1) de x = 100 a x = 105 e (2) de x = 100 a x = 101. (b) Encontre a taxa de varia¸ c˜ao instantˆ anea de f em rela¸c˜ao a x quando x = 100. [02] Considere a fun¸ c˜ao g cujo gr´ afico ´ e dado abaixo. Disponha os seguintes n´umeros em ordem crescente e explique seu racioc´ ınio: 0, g ( 2), g (0), g (2) e g (4). [03] Se a reta tangente ao gr´ afico da fun¸c˜ao y = f ( x ) em ( p, f ( p )) = (4 , 3) passa pelo ponto (0 , 2), calcule f (4) e f (4). [04] Quantas retas tangentes ao gr´ afico de y = x 3 + 3 x s˜ao paralelas ` a reta y = 6 x + 1? Determine as equa¸ c˜oes dessas tangentes.
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