Find an equation for this cubic curve.
Trang 1Created by T Madas
( ) 5 82
f x
x
′ = − , x ≠0
Find the value of f ( )4 , given that 2f ( )1 = +4 f ( )2
( )4 14
Question 24
( ) ( 2 )2
2
3x 2
f x
x
−
Show clearly that
( ) 2
1
11
f x dx =
proof
Trang 2Created by T Madas
1
2
(3 1)
y
x
+
= , x >0
Show clearly that
4
1
15
y dx =
proof
Question 26
Find the exact value of
3
1
4
3 x dx
x
−
giving the answer in the form p+q 3, where p and q are integers
6 2 3−
Trang 3Created by T Madas
Find the exact value of
2
2 1
3 2 x+ dx
giving the answer in the form a b+ 2, where a and b are integers
7 16 2+
Question 28
A cubic curve passes through the points P − −( 1, 9) and Q(2,6) and its gradient function is given by
2
dy
x kx
dx= + + , where k is a constant
Find an equation for this cubic curve
3 5 2 7 4
y=x − x + x+