gma00108-lista-12

# gma00108-lista-12 - DEPARTAMENTO DE MATEMTICA APLICADA GMA...

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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/ 12 Derivadas de ordem superior e o teorema da fun¸c˜ ao inversa [01] Calcule as derivadas primeira e segunda de cada uma das fun¸ c˜oes indicadas abaixo. (a) f ( x ) = x 5 + 6 x 2 7 x , (b) f ( t ) = t 8 7 t 6 + 2 t 4 , (c) y = cos(2 θ ), (d) y = θ sen( θ ), (e) F ( t ) = (1 7 t ) 6 , (f) g ( x ) = (2 x + 1) / ( x 1), (g) h ( u ) = (1 4 u ) / (1 + 3 u ), (h) H ( s ) = a s + b/ s , (i) h ( x ) = x 2 + 1, (j) y = xe cx , (k) y = tg(3 t ), (l) h ( x ) = arctg( x 2 ). [02] A figura abaixo exibe os gr´ aficos de f , f e f . Identifique cada gr´ afico. [03] A figura abaixo exibe os gr´ aficos de f , f , f e f . Identifique cada gr´ afico. 1

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[04] A figura abaixo exibe o gr´ afico de trˆ es fun¸c˜oes que descrevem a posi¸ c˜ao, a velocidade e a acelera¸ c˜ao de um carro em fun¸c˜ao do tempo. Identifique cada gr´ afico. [05] A figura abaixo exibe o gr´ afico de quatro fun¸c˜oes que descrevem a posi¸ c˜ao, a velocidade, a acelera¸ c˜ao e o arranco ( jerk ) de um carro em fun¸c˜ao do tempo. Identifique cada gr´
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