Question

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.

Tiles
f(x) = x2 + 3x
interval: [-2, 3]f(x) = 3x - 8
interval: [4, 5]f(x) = x2 - 2x
interval: [-3, 4]
f(x) = x2 - 5
interval: [-1, 1]
Sequence

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Answer 1

b,d,c,a

Explanation:

a)
`f(x) = x^2 + 3x`

interval: [-2, 3]

Average value =
`(f(b)-f(a))/(b-a)`

=
`(f(3)-f(-2))/(3-(-2)) =(18+2)/(5) -4`

b)
`f(x) = 3x - 8`

interval: [4, 5]

Average value =
`(15-7)/(1) =8`

c)

`f(x) = x^2 - 2x`

interval: [-3, 4]

Average value =
`(8-15)/(7) =-1`

d)
`f(x) = x^2 - 5`

interval: [-1, 1]

Average value =
`(-4+4)/(2) =0`

Hence arranging we get

b, d, c, a

Answer 2

we know that

The Average Rate of Change is the slope of a line or a curve on a given range. It is defined as the ratio of the difference in the function f(x) as it changes from 'a' to 'b' to the difference between 'a' and 'b'.

So

`A=((f(b)-f(a)))/((b-a))`

case a)
`f(x) = x^(2) + 3x`

in the interval
`[-2, 3]`

`a=-2\\ b=3\\ f(a)=(-2)^(2) +3*(-2)\\ f(a)=-2\\ f(b)=(3)^(2) +3*(3)\\ f(b)=18`

Find the Average Rate of Change

`A=((18-(-2)))/((3+2))`

`A=(20)/(5)`

`A=4`

case b)
`f(x) = 3x-8`

in the interval
`[4, 5]`

`a=4\\ b=5\\ f(a)=3*4-8\\ f(a)=4\\ f(b)=3*5-8\\ f(b)=7`

Find the Average Rate of Change

`A=((7-(4)))/((5-4))`

`A=(3)/(1)`

`A=3`

case c)
`f(x) = x^(2) -2x`

in the interval
`[-3, 4]`

`a=-3\\ b=4\\ f(a)=(-3)^(2) -2*(-3)\\ f(a)=15\\ f(b)=(4)^(2) -2*(4)\\ f(b)=8`

Find the Average Rate of Change

`A=((8-(15)))/((4+3))`

`A=(-7)/(7)`

`A=-1`

case d)
`f(x) = x^(2) -5`

in the interval
`[-1, 1]`

`a=-1\\ b=1\\ f(a)=(-1)^(2) -5\\ f(a)=-4\\ f(b)=(1)^(2) -5\\ f(b)=-4`

Find the Average Rate of Change

`A=((-4-(-4)))/((1+1))`

`A=(0)/(2)`

`A=0`

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval

so

the answer is

1)
`f(x) = x^(2) + 3x` ------->
`A=4`

2)
`f(x) = 3x-8` ----->
`A=3`

3)
`f(x) = x^(2) -5` ----->
`A=0`

4)
`f(x) = x^(2) -2x` ----->
`A=-1`