Question

Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.

0

1

2

7

Answer 1

to find the average rate use the formula to find the slope of the secant line going though f from x=0 to x=1.

that is \[\frac{f(1)-f(0)}{1-0}\]

Answer 2

f1/1?

Answer 3

f(0)=?

Answer 4

is my answer 1 ?

Answer 5

what is f(1)?
what is f(0)?

Answer 6

find f(x) when x = 1
find f(x) when x = 0

Answer 7

isn't the rate of change the derivative of the function?

Answer 8

yep
but it says average rate of change

Answer 9

which just calls for the slope formula without all the limit stuff

Answer 10

so what do i do..?

Answer 11

triciaal said you need to find f(x) when x=1 and also for x=0

Answer 12

then plug into the above formula i mentioned

Answer 13

@myininaya is your answer 7?

Answer 14

Let's go in steps @jenniferjuice
Can you find f(1)?

Answer 15

you said f(x)=-x^4+4x^3-2x^2+x+1
you should be able to replace all the x's there with 1's to find f(1)

Answer 16

like so f(1)=-1^4+4(1)^3-2(1)^2+1+1

Answer 17

now simplify that.

Answer 18

how?

Answer 19

what is 1^4?

Answer 20

\[f(1)=-1^4+4(1)^3-2(1)^2+1+1 \\ -1+4(1)^3-2(1)^2+1+1\]

so above i replaced 1^4 with 1

you should know what 1^3 and 1^2 is...

Answer 21

1^4=1*1*1*1=1
1^3=1*1*1=?
1^2=1*1=?
1 to any power equals?

Answer 22

1

Answer 23

right so replace the 1^n 's with 1

Answer 24

-1+4-2+2

Answer 25

\[f(1)=-1^4+4(1)^3-2(1)^2+1+1 \\ -1 +4(1)-2(1)+1+1\]
right -1+4-2+2
this can be simplified more

Answer 26

-1+4-2+2
-1+4-4
3-4
-1

Answer 27

-2+2 isn't 4 or -4

Answer 28

if you a credit of 2 then a debit of 2
then you have?

Answer 29

0

Answer 30

so -2+2 is 0

Answer 31

so -1+4 =?

Answer 32

3

Answer 33

right so f(1) is 3
what is f(0)?

Answer 34

f(0) should be the easiest to find

Answer 35

is it 0

Answer 36

nope

Answer 37

remember f(0) tells you to use the machine (function ) that is labeled f

Answer 38

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

Answer 39

to find f(0) replace every single x there with 0 then simplify

Answer 40

look if you replace all of those x's with 0
won't you just have 0+0-0+0+1?

Answer 41

yes so 1

Answer 42

@triciaal help here?

Answer 43

for f(1) you got 3 for f(0) you got 1
using the formula she originally gave f(1) - (f 0)divided by 1-0
it would be (3-1)/1 = 2

Answer 44

thanks for the medal