find the average rate of change of f(x)=x^2+4
a) from 1 to 3
b) from 0 to 2
c) from -2 to 1

Question

find the average rate of change of f(x)=x^2+4
a) from 1 to 3
b) from 0 to 2
c) from -2 to 1

anonymous · Answer

sure branson

anonymous · Answer

dy/dx=2x

parthkohli · Answer

Is it (x^2) + 4 or x^(2+4)

anonymous · Answer

2(3)-2(1)=4

anonymous · Answer

Two ways of doing it, plug in the limits of the interval to get y values, subtract them and divide by x (one end minus another). For instance:
f(1) = 1^2 + 4 =  5
f(3) = 3^2 + 4 = 13
f(3) - f(1) = 8
3-1 = 2
Avg rate of change is 8/2 = 4.

anonymous · Answer

The other way is to take the derivative and take the average distance (x=2 for the first interval), as Tai is doing :-)

anonymous · Answer

2(2)-2(0)=4

anonymous · Answer

cheers bmp

anonymous · Answer

Ok.. I thought that when you do the rate of change it would look something like this..
f(x)=x^2 + 4   when imputing a) (from 1 to 3) the Awnser would be something like ...
the average rate of change is from 5 - 13.
  I got that by...
f(x)=(1)^2 + 4 = 5
f(x)=(3)^2 + 4 =13     so wouldnt the awnser to a be 5 to 13? Or am I doing it wrong?

anonymous · Answer

ok

anonymous · Answer

ok??? What do you mean? =)
sorry Im just confused..lol

anonymous · Answer

No, you have to divide the x interval. You took sample points from 1 to 3, to it's 3-1. And similarly for the y-interval, you will get 13-5.

anonymous · Answer

Because you want the average, you are looking for a number, it's the average on a given interval. Remember:$$Slope = \frac{\Delta y}{\Delta x}$$This is the average rate of change. In general, you would take the derivative, but they are the same for the average case.

anonymous · Answer

Another way to think about it is to say "how fast is the function growing at a given point?" Your question is like that but with the change that you are asking is how fast the function is growing on average on a given interval. So, you want an average of the interval (halfway), that's why you have to subtract (or pick the midpoint for the derivative).

anonymous · Answer

So what is the actual awnser? It is giving me a place for 3 different awnsers...a,b,&c...hang on one second..I am trying tyo work it out

anonymous · Answer

For the first, it's 4.
For the second, it's 2.
For the last, it's 1.

anonymous · Answer

Typo, it's -1.

anonymous · Answer

yay...i checked my awnsers to your when I finished and I did it. Thank you so much! I wish you were my math teacher! =)

anonymous · Answer

You are welcome, but I am not good at teaching, haha.

anonymous · Answer

I can't tell hun!