c Find an equation of l1.. d Given that l1 is parallel to l2 show that an equation of l2 is y= x−... When t= the volume of a soap bubble is 91 cm and at that instant its volume is 3 decr
Trang 1The curve C has equation y= f x( ) given by
( ) 2( 2)3
f x = x− , 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= x−
( ) 2
f′ x = x − x+ , y=6x−16
Trang 2The point P(2,9) lies on the curve C with equation
y=x − x + x+ , x∈ , x≥ 1
a) Find an equation of the tangent to C at P , giving the answer in the form
y=mx+ , where c 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
+
y= x+
Trang 3The volume, V cm , of a soap bubble is modelled by the formula 3
( )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= the volume of a soap bubble is 91 cm and at that instant its volume is 3 decreasing at the rate of 6 cm per second 3
Determine the value of p and the value of q
p= q=