Question 1 (28 marks)
(a)
Use graphical software to graph the functionin the domain .
.
2
(b)
(i) On your graph of , plot the point Make sure that the point is exactly on the curve.
Use your graphical software to draw a tangent to the curve at point A.
Record the gradient of the tangent at point A in the table below.
(ii)
Slide the point A around the graph ofto the next x-value shown in the table below to determine the gradient of the tangent at this second point. (The tangent will move with the point.)
Repeat this process until you have completed the table.
x
16
9
4
1
0
1
4
9
16
Gradient of tangent (m)
-8
-6
-4
-2
0
2
4
6
8
(iii) Now, from your table, plot the ordered pairs (x, m) from the and
rows of your table onto a Cartesian Plane.
(iv) Join the points and give the equation of the graph formed by these points.
3
4
1
2
(c)
(i) Use the above process to investigate the gradients of the following functions:
A.
B.
C.
, where k is some constant.
x
-64
-27
-8
-1
0
1
8
27
64
Gradient of tangent (m)
-8
-6
-4
-2
0
2
4
6
8
x
-12
-9
-6
-3
0
3
6
9
12
Gradient of tangent (m)
3
3
3
3
3
3
3
3
3
x
3
3
3
3
3
3
3
3
3
Gradient of tangent (m)
0
...
