Bài tập Toán DIFFERENTIATION 09

Created by T. Madas
Question 4 (non calculator)
For each of the following curves find an equation of the normal to the curve at the
point whose x coordinate is given.

a)

f ( x ) = x3 − 4 x 2 + 1 , where x = 2

b) f ( x ) = x3 − 7 x 2 + 11x , where x = 3
c)

f ( x ) = 3 x 4 − 7 x3 + 5 where x = 2

d) f ( x ) = 1 x5 − 18 x + 11 where x = 2
4

Created by T. Madas

4 y = x − 30
4 y = x − 15
12 y + x + 34 = 0
2 y + x + 32 = 0


Created by T. Madas
Question 5 (non calculator)
For each of the following curves find an equation of the normal to the curve at the
point whose x coordinate is given.

a)

f ( x ) = 2 x3 − 3 x 2 − 10 x + 18 , where x = 2

b) f ( x ) = x3 − 4 x 2 + 6 x + 1 , where x = 1
c)

f ( x ) = 4 x3 + 2 x 2 − 18 x − 10 where x = −2

d) f ( x ) = −2 x3 + 4 x 2 − 1 , where x = 2

Created by T. Madas

x + 2y = 6
x+ y =5
22 y + x = 42
8 y = x − 10


Created by T. Madas
Question 6 (non calculator)
For each of the following curves find an equation of the normal to the curve at the
point whose x coordinate is given.

a) y = x 2 ( x − 6 ) +
3

b) y = 2 x 2 −

5
− 1 , where x = 1

x

16
, where x = 4
x

c) y = 4 x 2 + x

− 32

3

, where x = 1

d) y = 2 x 2 − 4 x 2 −

8
− 1 , where x = 4
x

Created by T. Madas

x − 14 y − 15 = 0

x + 7 y = 88

2 x + 13 y = 67

2 x + 9 y + 19 = 0