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Bài tập Toán DIFFERENTIATION 14
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Created by T. Madas
Question 3
The curve C has equation
y = 2 x2 − 4 x − 1 .
a) Find the gradient at the point on C , where x = 2 .
The point P lies on C and the gradient at that point is 2 .
b) Find the coordinates of P .
(
4 , P 3 ,− 5
2 2
Created by T. Madas
)
Created by T. Madas
Question 4
The curve C has equation
f ( x) = x +
1
, x ≠ 0.
x
a) Find the gradient at the point on C , where x = 1 .
2
The point A lies on C and the gradient at that point is 3 .
4
b) Find the possible coordinates of A .
( )
−3 , A 2, 5
2
Created by T. Madas
(
or A −2, − 5
2
)
Created by T. Madas
Question 5
The curve C has equation
y = x3 − x 2 − 5 x + 2 .
Find the x coordinates of the points on C with gradient 3 .
x = − 4 ,2
3
Question 6
The curve C has equation
y = x5 − 6 x3 − 3x + 25 .
Find an equation of the tangent to C at the point where x = 2 .
y = 5x − 7
Created by T. Madas
