Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: Sketching a Cubic Function - Worked Example
Description: Worked example of how to sketch a cubic function using a simple 5 step guide line. Ideal for 1st and 2nd year study of general and advanced mathematics degrees.
Description: Worked example of how to sketch a cubic function using a simple 5 step guide line. Ideal for 1st and 2nd year study of general and advanced mathematics degrees.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Example: Sketch y = (x + 1)2 (x -2)
STEP 1
...
Finding turning points (T
...
v
where u = (x + 1)2 and v = (x -2)
u’= 2(x + 1)
v’= 1
dy
u’
...
u
dx
= 2(x + 1)
...
(x + 1)2
= (x + 1)[ 2
...
Ps when
0
dx
(x + 1) [3x – 3] = 0
(x + 1) = 0 and [3x – 3] = 0
x = -1
3x = 3
x=1
When x = -1, y = (-1+1)2(-1+2)
=0
(-1, 0)
when x = 1 y = (2)2(-1)
= -4
(1, -4)
STEP 3
...
Ps
When x = -2,
When x = 0,
dy
+ve
dx
Max at (-1, 0)
dy
-ve
dx
Min at (1, -4)
dy
+ve
When x = 2,
dx
Or justify nature of the T
...
using a table of values to discuss the above
...
Extreme values
...
As x
y (x )3 (dominant term)
y
As x
y (x )3 (dominant term)
y
STEP 5
Title: Sketching a Cubic Function - Worked Example
Description: Worked example of how to sketch a cubic function using a simple 5 step guide line. Ideal for 1st and 2nd year study of general and advanced mathematics degrees.
Description: Worked example of how to sketch a cubic function using a simple 5 step guide line. Ideal for 1st and 2nd year study of general and advanced mathematics degrees.