Question

A function is given. Determine the average rate of change of the function between the given values of the variable.
f(x) = x + x4; x = −4, x = 3

Answer 1

sorry it should be f(x)= x+ x^4

Answer 2

anyone can help?

Answer 3

Average rate of change of a function f of an interval [a,b] is given by
\[\frac{f(b)-f(a)}{b-a}\]
In this case, the interval is (-4,3).

Answer 4

so should I graph this?

Answer 5

I tried pluging in and I ended up with 171/7

Answer 6

thats with b=3 and a =-4 like it should

Answer 7

The average value is
\[\frac{f(3)-f(-4)}{3-(-4)}=\frac{\left(3+3^4\right)-\left(-4+(-4)^4\right)}{3+4}\]
As far as I can tell, you don't have to do any graphing.

Answer 8

ya thats what I did

Answer 9

I'm not getting the same answer: http://www.wolframalpha.com/input/?i=%28%28b%2Bb%5E4%29-%28a%2Ba%5E4%29%29%2F%28b-a%29+when+a%3D-4+and+b%3D3

Answer 10

I messed up, I did it again and I got 168/7 but thats still wrong

Answer 11

negative

Answer 12

The numerator can be kinda tricky:
\[(3+3^4)-(-4+(-4)^4)\\
(3+81)-(-4+256)\\
84-252\\
-168\]
And divided by 7, you have -24.

Answer 13

ya I forgot to put the negative im sorry thanks again but u know what it is, I dont put it out in steps like that like I should so I completely got wrong answers the first couple times because of the sign change from the minus. THe way I normally do it is I do one tyerm first on a seperate part of the paper then the other like under it or something and then bring everything down.