Answer:
Step-by-step explanation:
If x is -1, then the point on the parabol is (-1,4)
If x is 0, then the point on the parabol is (0,-2)
If x is 1, then the point on the parabol is (1,-6)
Using derivatives, it is found that the best estimate of f '(2) based on this table of values is of 10.
The rate of change <u>from x = 0 to x = 2</u> is given by:

From <u>x = 2 to x = 4</u>, it is given by:

The average of these rates is:

Hence, the best estimate of f '(2) based on this table of values is of 10.
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Answer:
The ratio of AC/CB=1/3
Step-by-step explanation:
We use the section formula:

We substitute the point A(-1.5,0) and B(4.5,8).
We plug in the points to get:

This is supposed to be equal to: (0,2).

We can equate, corresponding coordinates to find m and n.

This implies that:




Therefore the ratio is m:n=1:3
Answer:
A maximum of 43 students and 11 teachers can go to the trip.
Step-by-step explanation:
Since a group of teachers and students will take a bus trip to a museum, and each teacher will lead a group of no more than 4 students, and the bus can hold a maximum of 54 teachers and students, to determine the possible numbers of teachers and students who can go on the trip, the following calculation must be performed:
4 + 1 = 5
54/5 = X
10.8 = X
10 x 4 = 40
10 x 1 = 10
4 - 1 = 3
Therefore, a maximum of 43 students and 11 teachers can go to the trip.