ExercciosderivadasI

Prévia do material em texto

1) Dada a função do 1º grau f ( x ) = 2 x – 3, calcule: 
 
a) f ′(2) = c) f ′( -1) = 
 
b) f ′(5) = d) f ′(- 3) = 
 
2) Calcule o valor numérico das derivadas: 
 
a) y = 2 x 
3
 + 3 x 
2
 – 4 x + 1 y ′ ( 1 ) = 
 
b) y = 5 x 
4
 – 2 y ′ ( - 1 ) = 
 
c) f ( x ) = x 
2
 – 2 x f ′ ( 2 ) = 
 
d) f ( x ) = 
32
3
2
 x
x
 f ′ ( 1 ) = 
 
e) y = 8 x ( 3 x + 2 ) y ′ ( 0 ) = 
 
f) f ( x ) = ( 2 x + 4 ) ( 3 x – 4 ) f ′ ( - 1 ) = 
 
g) y = 3 x 
2
 – 1 y ′ ( - 1 ) = 
 
h) y = x 
3
 + x 
2
 – x + 5 y ′ ( - 2 ) = 
 
i) f ( x ) = ( 3 x + 5 ) 
3
 f ′ ( - 1 ) = 
 
j) y = ( 2 x 
2
 – x + 1 ) 2 y ′ ( 3 ) = 
 
l) f ( x ) = 
3
18
3
5
9
127
3
3
7 3
679

x
x
xxx
 f ′ ( - 1 ) = 
 
m) y = ( 5 x 
4
 – 8 ) 4 y ′ ( 1 ) = 
n) ) y = 54
6
2
7






 x
x y ′ ( 0 ) = 
o) f ( x ) = 3 x 
4
 . ( 7 x 
2
 – 5 ) f ′ ( 1 ) = 
 
p) f ( x ) = ( 7 – 10 x 2 ) ( - 8 x + 4 x 3 ) 3 f ′ ( 0 ) = 
 
q) f ( x ) = - 8 x 
4
 . ( 4 x + 1 ) 
5
 f ′ ( -1 ) = 
 
3) Calcule a derivada nos pontos: 
 
a) f ( x ) = x 
2
 + 1 no ponto x = 5 
 
b) f ( x ) = 3 x 
2
 no ponto x = 2 
 
c) f ( x ) = 2 x 
3 
 no ponto x = 1 
 
d) f ( x ) = 2 x 
3
 – 2 no ponto x = 3 
 
e) f ( x ) = x 
3
 + 4 x no ponto x = 2 
 
f) f ( x ) = 78
3
4
5






 x
x no ponto x = 1 
g) f ( x ) = 
5
12
2
3
6
97
2
3
4 3
679

x
x
xxx
 no ponto x = - 1 
 
h) f ( x ) = ( 4 x 
3
 – 3 ) ( - 6 x 2 + 4 x ) 6 no ponto x = 1 
 
 
4) Considere f ( x ) = 2 x 
3
 + 15 x 
2
 + 12 x, determine f ′ ( 1 ) = 
 
 
 
5) Sendo f ( x ) = 2 x 
3
 – 15 x 2 + 36 x – 7 e g ( x ) = x 3 – 6 x 2 + 11 x – 6 , determine : 
 f ′ ( 0 ) - 2 g ′ ( 1 ) = 
 
 
 
6) Dada a função f ( x ) = 3 x 
2
 – 1, calcule f ′ ( - 4 ) = 
 
 
 
7) Calcule a derivada de f ( x ) = ( x 
2
 – 3 x ) 3 e encontre f ′ ( 2 ) = 
 
 
 
8) Calcule a derivada de f ( x ) = ( x 
3
 – 2 x ) 2 e encontre f ′ ( - 2 ) = 
 
 
 
 
 
 
RESPOSTAS: 
1) a) 2 b) 2 c) 2 d) 2 
 
2) a) 8 b) – 20 c) 2 d) - 
3
4
 
 e) 16 f) -8 g) – 6 h) 7 
 
 i) 36 j) 352 l) - 
6
47
 m) 2160 
 
 n) -30 o) 66 p) - 168 q) - 20736 
 
3) a) 10 b) 12 c) 6 d) 54 
 
 e) 16 f) - 
4
343
 = - 85,75 g) - 
6
43
 h) - 768 
 
4) 48 5) 32 6) – 24 7) 12 
 
 8) - 80