Find the average rate of change of f ( x ) = -2x^2 + 4x + 2 as x varies from 1.2 to 3.8

Here we need to find the average rate of change of .

Now,

Let us find out the value of at the point .

Plugging in the equation we get:

So,

Now calculating the value of at .

So,

Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:

, where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.

Therefore,

So, the average rate of change of the function from 1.2 to 3.8 is .

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."