Year 12 Homework Assignment 4.2 Diff 1.docx, Exams of Mathematics

exam qus on differentiation for a level

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2025/2026

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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)

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Year 12 Homework Assignment 4. Differentiation 1

1) Find

dy

dx

and

d

2

y

d x

2 for each of the following

b) c) d) e) f)

The curve C has equation y = 4 x + 3 x

3 2

– 2 x^2 , x > 0.

a) Find an expression for

dy

dx .

( b) Show that the point P(4, 8) lies on C.

( c) Show that an equation of the normal to C at the point P is

3 y = x + 20.

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.