Exercício de Matemática_Funções_Derivadas
Autor: DAMYAOONLINE | Publicado: 2011-07-30T16:49:00-07:00


1. Classifique as funções abaixo em crescente ou decrescente:&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; a) Y = 3X + 2&nbsp; &nbsp; &nbsp; b) Y = -2X2&nbsp; &nbsp;- 3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2.&nbsp; Calcule x’ e x” nas equações abaixo:a)&nbsp;&nbsp;&nbsp; x2 + 4x + 2 = 0b)&nbsp;&nbsp;&nbsp; 2x2 + 4x + 2 = 0
3. Resolva as inequações abaixo:a)&nbsp;&nbsp;&nbsp; 2x2 - 5x + 2 &gt; 0b)&nbsp;&nbsp;&nbsp; 4 ≤ x2 ≤ 9c)&nbsp;&nbsp;&nbsp; ( 1 - 4x2 ) . ( 2x2 + 3x ) &gt; 0d)&nbsp;&nbsp;&nbsp; ( 4x2 + x – 5 ) : ( 2x2 – 3x – 2 ) &gt; 0
4. Calcule os pontos de máximo e de mínimo das parábolas abaixo:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a)&nbsp; x2 + 4x – 8 = 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; b)&nbsp; - 2x2&nbsp; - 4x + 16 = 0&nbsp;&nbsp;&nbsp; 5. Dadas as funções f(x) = 5x2 + 2x - 7, com x € R e g(x) = 4x + 1, com x € R, o valor de f(g(-8)) é igual a.&nbsp; 
6. Tio João possui uma fábrica de sorvetes. Mensalmente são vendidos, em média, 600 caixas de picolés pelo preço de R$ 30,00 cada. Com o objetivo de incentivar o aumento da venda do número de caixas de sorvetes, Tio João observa que cada R$ 1,00 diminuído no preço da caixa, ele vende 30 caixa a mais. Sendo assim, quanto Tio João deveria cobrar pela caixa para que sua receita fosse máxima?


7. Classifique as funções abaixo em injetora, sobrejetora ou bijetora.
-&nbsp; Dizemos que uma função f é injetora quando para todo (x1&nbsp; e x2 ) € D , se (x1 ≠ x2)implica que f(x1 ) ≠ f(x2 ). -&nbsp; Dizemos que uma função f é sobrejetora quando o seu conjunto imagem é igual aocontradomínio.-&nbsp; Dizemos que uma função é bijetora quando ela é injetora e sobrejetora ao mesmotempo.
7.1.) Seja as funções abaixo, definidas em R, Construa os gráficos e classifique-as em injetora, sobrejetora, bijetora ou nem injetora nem sobrejetora.
a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f(x) = 2xb)&nbsp;&nbsp;&nbsp;&nbsp; f(x) = f(x) = x2 – 2c)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f(x) = | x |&nbsp;d)&nbsp;&nbsp;&nbsp;&nbsp;  f(x)&nbsp; = sen(x)
8. Seja a função f(x), definida nos reais, tal que f(x) = 5x4 + 2x2 – 4, o valor de f’”(2) é igual a...
9. Se f(x) = cos(x), então a derivada fV (x) é:

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&nbsp;&nbsp;&nbsp; 10.&nbsp; A equação da velocidade de uma partícula que se movimenta segundo a lei horária s = f(t)&nbsp; é dada por&nbsp; v = f’ (t). Sabendo&nbsp; que um móvel se movimenta&nbsp; segundo&nbsp; a função horária&nbsp; s(t) = 4t2 + 6t + 5,&nbsp; com “s”&nbsp; em metros e “t” em segundos obtenha a velocidade deste móvel no instante t = 12s.

11. A equação e o coeficiente angular da reta que passa pelos pontos ( 6 , 4 ) e (&nbsp; 8 , 6 )&nbsp;
são respectivamente iguais a...&nbsp;&nbsp;&nbsp;&nbsp; 
12. Sendo f(x) = x3 &nbsp;+ x&nbsp; ,&nbsp; g(x) = x + 1&nbsp;&nbsp;&nbsp; e&nbsp; &nbsp;h(x) = f(x) . g(x), o valor de h’(2) vale...

&nbsp;Professor: Damião Batista