Question

Find the average rate of change of f(x)= 7x^2+30

Answer 1

@agent0smith @amistre64

Answer 2

please anyone just need a step by step

Answer 3

hmm... ok, so do you know where to start off?

Answer 4

no can you help me @Clalgee can you do it step by step so i can take notes and do my other simmilair question?

Answer 5

@nincompoop can you help me?

Answer 6

The Average Rate of Change function describes the average rate at which one quanity is changing with respect to something else changing.

Answer 7

can you show me step by step so i can do the other one by myself?

Answer 8

In general, an average rate a change function is a process that calculates the the amount of change in one item divided by the corresponding amount of change in another. Using function notation, we can define the Average rate of Change of a function f from a to x as

\[A(x)=\frac{ f(x)-f(a) }{ x-a }\]

Answer 9

A is the name of this average rate of change function
x - a represents the change in the input of the function f
f(x) - f(a) represents the change in the function f as the input changes from a to x


a few examples to start:
Find the slope of the line going through the curve as x changes from 3 to 0.

Step 1: f (3) = -1 and f (0) = -4

Step 2: Use the slope formula to create the ratio

\[\frac{ f(0)-f(3) }{ 0-3 }\]

Step 3: Simplify.

\[\frac{ f(0)-f(3) }{ 0-3 }=\frac{ -4-(-1) }{ 0-3 }=1\]

Step 4: So the slope of the line going through the curve as x changes from 3 to 0 is 1.

Answer 10

ohh okay so would the rate of change be increasing or decreasing?

Answer 11

sec...

Answer 12

fo can you tell me where my 7x^2 and 30 fit into the formula?

Answer 13

had to get my graphing calc

Answer 14

in your question do they state x=? and x=?

Answer 15

find the AROC of (7x^2)+30 from x= something to x= something

Answer 16

let me show you my question i have graph also

Answer 17

that is a weird question for sure

Answer 18

yes i dont understadn it i have the graph i need to find the rate of change and see if its increasing or decreasing

Answer 19

let me find my old book and see what it says brb

Answer 20

so i think they want you to use the above formula, and substitute x values

Answer 21

for instance when x= -0.5 and x=1

Answer 22

that will give you an AROC

Answer 23

\[AROC= \frac{ f(-0.5)-f(1) }{ (-0.5)-1() }\]

Answer 24

f(-0.5)= 7((-0.5)^2)+30 =

and

f(1)= 7((1)^2)+30 =

Answer 25

\[\frac{ f(-0.5)-f(1) }{ -0.5-1 }=\frac{31.75-37 }{ -0.5-1 }=\frac{ -5.25 }{-1.5 }\]

Answer 26

AROC = 3.5

Answer 27

increasing with justification :)

Answer 28

you can try it again with any other x values, for practice, then substitute into your equation

Answer 29

oh k tahnks :)

Answer 30

np