<< Chapter < Page | Chapter >> Page > |
Fill in the table by calculating the average gradient over the indicated intervals for the function :
A-B | |||||
B-C | |||||
C-D | |||||
D-E | |||||
E-F | |||||
F-G |
What do you notice about the average gradient over each interval? What can you say about the average gradients between A and D compared to the averagegradients between D and G?
The average gradient of a parabolic function depends on the interval and is the gradient of a straight line that passes through the points on the interval.
For example, in [link] the various points have been joined by straight-lines. The average gradients between the joined points are then the gradients of the straight lines that pass through the points.
Given the equation of a curve and two points ( , ):
Find the average gradient of the curve between the points and
Label the points as follows:
to make it easier to calculate the gradient.
We use the equation for the curve to calculate the -value at and .
The average gradient between and on the curve is 0.
Notification Switch
Would you like to follow the 'Siyavula textbooks: grade 10 maths [ncs]' conversation and receive update notifications?