Year 12 Homework Assignment 4.2
Differentiation 1
1) Find
dy
dx
and
d
2
y
d x
2
for each of the following
b)
c)
d)
e) f)
2)
3)
4)
5)
The curve
C
has equation
y
= 4
x
+
3
x
3
2
– 2
x
2,
x
> 0.
a
) Find an expression for
dy
dx
.
(3)
(
b
) Show that the point
P
(4, 8) lies on
C
.
(1)
(
c
) Show that an equation of the normal to
C
at the point
P
is
3
y
=
x
+ 20.
(4)
The normal to
C
at
P
cuts the
x
-axis at the point
Q
.
(
d
) Find the length
PQ
, giving your answer in a simplified surd form.
(3)
6)
