Find the average rate of change of f(x) with respect to x on the interval.

-1

Step-by-step explanation:

The average rate of change is synonymous to the slope.

In other words, the find the average rate of change in a given interval, find the two points defined by the interval and then find the slope between them.

So, we have the function:

defined by the interval:

So, find the values of f(x) at each of these bounds.

For -4, plug in -4 for x:

Therefore, the first point is (-4,12).

Now, plug in 3 for x:  

Our other point is (3,5).

Now, find the slope between them to get the average rate of change. The slope formula is:

Let (-4,12) be x₁ and y₁ and let (3,5) be x₂ and y₂. Therefore:

Therefore, the average change between the interval is -1.

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get

your answer is

a.

5

step-by-step explanation: