Question

What is the average rate of change of the function f(x)= X^2-4x+7 on the interval 1 14 years ago

Answer 1

basically its the slope formula:

f(3) -f(1)/ 3-1

Answer 2

how did u get that?

Answer 3

find f(1) and f(3) average rate of change is

\[m = [(f(3) - f(1)]/(3 - 1)\]

Answer 4

rate of change = slope

technically avg rate of change is defined as:
\[\frac{1}{b-a}\int\limits_{a}^{b} f'(x) dx = \frac{f(b) -f(a)}{b-a}\]

Answer 5

so can i use

m= Y2-Y1/X1-X2
?

Answer 6

yep
the avg slope in that interval is the same as the slope of the line connecting the 2 endpoints

Answer 7

0/2 ?

Answer 8

ok yeah thats it.

0/2 = 0
so the avg slope is 0

Answer 9

g(x)=mx+b, x1<x<x2

Answer 10

Without doing any calculation, how can one determine the average rote of change of g(x)= mx+b over the interval X1<X<X2 ?

Answer 11

just plug it into the formula

g(x2)-g(x1)/ x2-x1

Answer 12

and then ?

Answer 13

finish?

Answer 14

simplify, you should find that things cancel

Answer 15

mX2-mX1/X2-X1 ?

Answer 16

yep, now factor out the m

Answer 17

answer is m ?

Answer 18

yep :)

Answer 19

If f(x)=1/3^x and g(x)=x^3, what is the domain of (f.g)(x)?

Answer 20

(f into g)(x)

Answer 21

{x E R} ?

Answer 22

so you are plugging g(x) into the variable for f

--> 1/3^g(x) = 1/3^(x^3)

domain is all possible x_values

Answer 23

(f.g)(x)

divided

Answer 24

f(x).g(x)

Answer 25

multiply

Answer 26

??

Answer 27

f(x) and g(x) are multiply

Answer 28

1/3^x * x^3

Answer 29

yeah

Answer 30

thats it

Answer 31

what is the domain?

Answer 32

oh, all real num

there is no x value that makes it undefined

Answer 33

{x E R} ?
x is not equal -1 ?

Answer 34

umm well R is used as notation for the set of all real numbers

Answer 35

i mean x can't be equal -1 or x can't be equal 0 or x can't be equal 1 or
just { x E R } ?