Question

a ball is thrown upward from the top of a building, the function below shows the height of the ball above the ground f(t)in feet at different times (t) in seconds:

f(t)=-16t^2+32t+90

the average rate of change of f(x) from x=4 to x=6 is?

Answer 1

@ranga

Answer 2

@sourwing

Answer 3

Isn't it just (f(6) - f(4))/2?

Answer 4

im not sure @IAmSinged

Answer 5

@iambatman

Answer 6

yeah it's just the change in f(x) divided by the change in x.
http://tutorial.math.lamar.edu/Classes/CalcI/Tangents_Rates.aspx

Answer 7

wait so you just dived 4 by 6?

Answer 8

@jim_thompson5910

Answer 9

You're finding the slope between the 2 pts.
I know the change in y (f(6) - f(4)), and I know the change of x (6 - 4 = 2).
Then I just divide the change in y by the change in x, because that's the definition of the slope.

Answer 10

im confused :/

Answer 11

You want to find the slope between the points at t = 4 and t = 6 (definition of average rate of change). You get the y values of the points by plugging it into the equation. At t = 4, we get -38. At t =6, we get -294.
So we have the points (4, -38) and (6, -294) and we want to find the slope.
So we do:
(-294 + 38)/(6 - 4) = -128.

Answer 12

The average rate of change of a function, f(x), between x = a and x = b is defined as:
\[\frac{f(b) - f(a)}{b-a}\]

Answer 13

You can prove that the slope between the two points is the average rate of change by finding the derivative divided by the change in x, and then integrating it.

Answer 14

@ranga so I would plug In 4 and 6? f(4)-f(6) /4-6

Answer 15

Yes, but I would do it the other way (you will get the same answer):
{ f(6) - f(4) } / { 6 - 4}

Answer 16

is the answer 1?

Answer 17

@ranga ?

Answer 18

No, that is not the answer.
f(6) = ?
f(4) = ?

Answer 19

6 and 4 right?

Answer 20

f(t)=-16t^2+32t+90
f(6) = -16(6)^2 + 32(6) + 90 = ?
f(4) = -16(4)^2 + 32(4) + 90 = ?

Answer 21

f(6)=-294
f(4)=-38

Answer 22

Yes. Plug it into \[\frac{f(6) - f(4)}{6-4}\]

Answer 23

-294 - (-38) /-294 -(-38) =-256/-256?

Answer 24

\[
\frac{f(6) - f(4)}{6-4} = \frac{-294+38}{2} = \frac{-256}{2} = -128 ~ft./sec
\]

Answer 25

ohhhhh