Question

Find the average rate of change
f(x)=x^3-3x+9

(a) from 5 to 9

Answer 1

College Algebra

Answer 2

Use the formula

m = ( f(x2) - f(x1) )/( x2 - x1 )

where

m = average rate of change
x1 = first x value
x2 = second x value
f(x) is any function

Answer 3

RONNCC you're thinking of the average of the function from x = 5 to x = 9

NOT the average rate of change from x = 5 to x = 9

Answer 4

the two are completely different things

Answer 5

Yea I tried plugging both in but still couldn't figure it out. ;(

Answer 6

m = ( f(x2) - f(x1) )/( x2 - x1 )

m = ( f(9) - f(5) )/( 9 - 5 )

Answer 7

m = ???

Answer 8

Dont I need to know f first?

Answer 9

f(x)=x^3-3x+9

Answer 10

that's given

Answer 11

I got all reals...

Answer 12

@jim_thompson5910 nvm. it makes little sense why you would want to do that. your way is likely what is wanted.

Answer 13

I'm not sure what you mean by the average of the derivative

Answer 14

I am confused now

Answer 15

f(x)=x^3-3x+9

f(9)=(9)^3-3(9)+9

f(9) = ???

Answer 16

so you're drawing a line from the beginning to the end, well how much is that line changing usually per unit 'x'? that's the average. so in this case (f(9)-f(5)) / (9-5) if you draw it out it may help

Answer 17

711

Answer 18

huh?

Answer 19

f(9)=711

Answer 20

@jim_thompson5910

Answer 21

f(5) = ???

Answer 22

119

Answer 23

@jim_thompson5910 f(5)=119

Answer 24

so put this all together to get

m = ( f(x2) - f(x1) )/( x2 - x1 )

m = ( f(9) - f(5) )/( 9 - 5 )

m = ( 711 - 119 )/( 9 - 5 )

m = ???

Answer 25

148

Answer 26

yup!

Answer 27

Sweet!