Gradient Function Investigation
Gradient Function
In this investigation I am going to investigate the gradients of the
graphs Y=AXN Where A and N are constants. I shall then use the
information to find a formula for all curved graphs.
To start the investigation I will draw the graphs where A=1 and N= a
positive integer.
Y=X2
X
Height
Width
Gradient
1
1
0.5
2
2
4
1
4
3
9
1.5
6
4
16
2
8
Looking at the results above I can see that the gradient is twice the
X value, the height is X2 and the width is 1/2 the X value. This shows
me that there are several patterns in the graph but there is not
enough to make a formula on so I am going to do another graph
Y=X3
X
Height
Width
Gradient
1
1
0.33
3
2
8
0.66
12
3
27
1
27
4
64
1.33
48
There are some more patterns in this table, the height is now X3 and
the width is 1/3 of the X value. I can see no pattern between the
Gradient and the X value in this table.
By comparing the two tables I can see that the height is what Y equals
(AXN) and the width is the 1 over the power (X/2 for X2 and X/3 for X3).
So if the formula for the gradient is Height/Width then, by replacing
the height with AXN and the width with X/N we get XN/(X/N). We can
simplify this by multiplying both sides by N to get ANXN/X and we can
simplify this by dividing both sides by X to get ANXN-1.
I shall now you this formula in the graph Y=X4 to test it.
= ½ (a2 + b2) ´ ½ (a2 + b2) eventhough it would be easier to do ab,
What is the difference between a.. Repeat step 4 twice more so you end up with three results. the same height then continue onto step 9. 9. What is the difference between a'smart' and a ' Add all these results together and divide the answer by three to obtain the average of the. 10. What is the difference between a'smar Record this average in the table.
2. Width of the base which divided to 3 groups: 1: More than 5 mm; 2: between 3-5 mm; less than 3 mm.
Use millimeter ruler to measure the wooden block used in part B of this procedure to get length, width, and depth.
To solve this problem, I built different sized cubes (2 x 2 x 2, 3 x 3
Since it is hard to make calculations with real years, I created a graph of height against years since 1932. When considering the trends line and possible equation of this graph models.
from 10cm to 50cm to make it easier to see the difference in a graph.
Use the caliper to and pull it on the nose and the back of the skull.Then take that measurement and write it down on the table as the height
This graph shows the result that I expect to get, I expect to see a
* Surface Area - This will not affect any of my results, as we are
If I were using a cut out of length 1cm, the equation for this would
1/do + 1/di = 1/ 1/distance from object + 1/distance from image = 1/focal length
first column I have the number of cubes and in the second I have the
The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”.