- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập Toán DIFFERENTIATION 23
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (438.25 KB, 3 trang )
Created by T. Madas
Question 31
The curve C has equation y = f ( x ) given by
3
f ( x ) = 2 ( x − 2) , x ∈ » .
a) Sketch the graph of f ( x ) .
b) Find an expression for f ′ ( x ) .
The point P ( 3, 2 ) lies on C and the straight line l1 is the tangent to C at P .
c) Find an equation of l1 .
The straight line l2 is another tangent at a different point Q on C .
d) Given that l1 is parallel to l2 show that an equation of l2 is
y = 6x − 8 .
f ′ ( x ) = 6 x 2 − 24 x + 24 , y = 6 x − 16
Created by T. Madas
Created by T. Madas
Question 32
The point P ( 2,9 ) lies on the curve C with equation
y = x3 − 3 x 2 + 2 x + 9 , x ∈ » , x ≥ 1 .
a) Find an equation of the tangent to C at P , giving the answer in the form
y = mx + c , where m and c are constants.
The point Q also lies on C so that the tangent to C at Q is perpendicular to the
tangent to C at P .
b) Show that the x coordinate of Q is
6+ 6
.
6
y = 2x + 5
Created by T. Madas
Created by T. Madas
Question 33
The volume, V cm3 , of a soap bubble is modelled by the formula
2
V = ( p − qt ) , t ≥ 0 ,
where p and q are positive constants, and t is the time in seconds, measured after a
certain instant.
When t = 1 the volume of a soap bubble is 9 cm3 and at that instant its volume is
decreasing at the rate of 6 cm3 per second.
Determine the value of p and the value of q .
p = 4, q = 1
Created by T. Madas
