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Bài tập Toán DIFFERENTIATION 08
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Created by T. Madas
Question 1 (non calculator)
For each of the following curves find an equation of the tangent to the curve at the
point whose x coordinate is given.
a) y = x 2 − 9 x + 13 , where x = 6
y = 3 x − 23
b) y = x 4 + x + 1 , where x = 1
y = 5x − 2
c) y = 2 x 2 + 6 x + 7 , where x = −1
y = 2x + 5
d) y = 2 x3 − 4 x + 5 , where x = 1
y = 2x + 1
e) y = 2 x3 − 4 x 2 − 3 , where x = 2
y = 8 x − 19
f)
y = 3x3 − 17 x 2 + 24 x − 9 , where x = 2
Created by T. Madas
y = −8 x + 11
Created by T. Madas
Question 2
(non calculator)
For each of the following curves find an equation of the tangent to the curve at the
point whose x coordinate is given.
f ( x ) = x3 − 4 x 2 + 2 x − 1 , where x = 2
y = −2 x − 1
b) f ( x ) = 3 x3 + x 2 − 8 x − 5 , where x = 1
y = 3 x − 12
a)
c)
f ( x ) = 2 x3 − 5 x 2 + 2 x − 1 , where x = 2
d) f ( x ) = x3 − x 2 − 3 x − 2 , where x = 1
e)
f ( x ) = 2 x3 + x 2 − 2 x − 2 , where x = 1
Created by T. Madas
y = 6 x − 13
y = −2 x − 3
y = 6x − 7
Created by T. Madas
Question 3
(non calculator)
For each of the following curves find an equation of the tangent to the curve at the
point whose x coordinate is given.
3 1
a) y = x 2 − − , where x = −2
x 2
b) y = x3 − 6 x +
8
+ 1 , where x = 2
x
c) y = 4 x 2 +
5
− 1 , where x = 1
x
d) y = 2 x −
6
, where x = 4
x
3
e) y = 3 x 2 −
32
, where x = 4
x
Created by T. Madas
13 x + 4 y + 6 = 0
y = 4x − 7
y = 3x + 5
7 x − 8 y − 20 = 0
y = 11x − 28
