Question

Help please? Fan&&Medal

Is rate of change, and changing the constant the same thing? I'm confused...

Answer 1

is the a more full question that this is from?

Answer 2

rate of change has to do with slopes, constants have to do with vertical displacements

Answer 3

I have a function f(x)=2(x-11)^2 +3 , and my question is Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Answer 4

oh, then you want to find the average rate of change (the slope of the line) between the stated points.

Answer 5

find (4,f(4)) and (7,f(7))

then determine the slope of the line that connects them

Answer 6

Average rate of change for f(x) from x = 4 to x = 7 =

\(\Large \frac{f(7) - f(4)}{7-4} = ?\)

Answer 7

Sooo, I plug in (4,f(4)) and (7,f(7)) to my function?? Or..

Answer 8

f(a) = 2(a-11)^2 + 3
f(b) = 2(b-11)^2 + 3

f(a) - f(b)

[2(a-11)^2 + 3] - [2(b-11)^2 + 3]

2(a-11)^2 + 3 -2(b-11)^2 - 3

2(a-11)^2 -2(b-11)^2

2 [(a-11)^2 - (b-11)^2]

now we have a difference of squares ...

2 [(a-11) - (b-11)] [(a-11) + (b-11)]

2 (a-11-b+11) (a-11+b-11)

2 (a-b) (a+b)

Answer 9

well, yeah. using the slope formula, or definition

the change in f(x) as x moves from 4 to 7, divided by the change from 4 to 7

\[\frac{f(4)-f(7)}{4-7}\]

Answer 10

ironically, we have a-b on the denominator so this simplifies to just 2(a+b)

Answer 11

ohhh, okay!! :)) Thank you!