Question

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.
f(x) = 1(x - 3)^2 + 10

Answer 1

Medals given

Answer 2

@zepdrix ?

Answer 3

Calculate the function values for x=4 and x=7,
Take their difference,
then divide that difference by the difference in the x values.

Wow I said difference a lot +_+

Answer 4

For linear functions, the rate of change is constant (always stays the same).
So this formula might look familiar:\[\Large\rm m=\frac{f(x_2)-f(x_1)}{x_2-x_1}\]
For non-linear functions, we call it an average rate of change,\[\Large\rm m_{ave}=\frac{f(7)-f(4)}{7-4}\]It only applies to this specific interval.

Answer 5

f(4) = 1(4 - 3)^2 + 10 = (4 -3)(4 - 3) + 10 = 12 + 10 = 22
f(7) = 1(7 - 3)^2 + 10 = (7 - 3)(7 - 3) + 10 = 56 + 10 = 66

then its... 66 - 22 / 7 - 4 which is 44 / 3 which is... 14.6666667 ish or 14 2/3??

Answer 6

@zepdrix ?

Answer 7

Sorry one sec :)

Answer 8

its good.

Answer 9

\[\Large\rm f(4) = 1(\color{red}{4 - 3})^2 + 10\]Do this part in red first.
Don't expand out the square first.

Answer 10

ohhh ok. Lol i see now.

Answer 11

f(4) = 1 + 10 = 11
and f(7) = 4^2 + 10 = 16 + 10 = 26

so 26 - 11 / 7 - 3 = 15 / 4 = 3 3/4?

Answer 12

Woops, the denominator is 7-4, right?

Answer 13

uhh yeah

Answer 14

oh lol lemme fix that

Answer 15

so its 15/3 which is 5

Answer 16

Yay good job \c:/

Answer 17

Thank you so much!