Calculate the average rate of change for the function f(x) = -x^4 + 4x^3 - 2x^2 + x + 1, from x = 0 to x =1
Options
1)0
2)1
3)2
4)7

Question

Calculate the average rate of change for the function f(x) = -x^4 + 4x^3 - 2x^2 + x + 1, from x = 0 to x =1
Options 
1)0
2)1
3)2
4)7

amistre64 · Answer

any ideas?

amistre64 · Answer

an average rate of change is simply the slope of the line between 2 points ...

anonymous · Answer

i have no idea this problem makes no sense to me @amistre64

amistre64 · Answer

so, you have no idea how to find the slope between 2 points?

anonymous · Answer

no

amistre64 · Answer

well, there is something called a slope formula.  it is the change in y, divided by the change in x.  let x move from a to b, then y moves from f(a) to f(b) and we get:
$$slope=\frac{f(a)-f(b)}{a-b}$$

anonymous · Answer

how do i know what numbers to plug in?

amistre64 · Answer

they define f(x) for you already, and tell you that x is from 0 to 1.

amistre64 · Answer

$$\frac{f(0)-f(1)}{0-1}$$

anonymous · Answer

wouldnt that be -1

amistre64 · Answer

dunno. i havent tried to work it yet :)

amistre64 · Answer

f(0) =  1
f(1) =  -1 + 4 - 2 + 1 + 1 = 3

1-3
--- = 3
0-1

amistre64 · Answer

im going with no, its not -1

anonymous · Answer

so its 3?

amistre64 · Answer

maybe .... hard to tell if i know how to add correctly or not these days

anonymous · Answer

or is it 2?

amistre64 · Answer

2 is better, yes

anonymous · Answer

thank you!!

anonymous · Answer

i have one more question

amistre64 · Answer

:)  youre welcome

anonymous · Answer

Given the function f(x) = -3x3 + 9x2 - 2x + 3, what part of the function indicates that the left end starts at the top of the graph?

anonymous · Answer

1)	The degree of the first term
	2)	The degree of the last term
	3)	The coefficient on the first term
	4)	The coefficient of the last term

amistre64 · Answer

that question is not a good question.  there is no 'start' of the graph unless something about it is restricted.  and since different restrictions will produce different 'left side starts' the question is patently absurd.

anonymous · Answer

so theres no way to answer it?

amistre64 · Answer

there is no way to answer it intelligently since the person that made the question evidently had no idea what they were asking for.

amistre64 · Answer

spose i ask you:  how do i get from here to there?

what is missing about the situation that prevents you from giving a sensible response?

anonymous · Answer

the numbers

amistre64 · Answer

well, more accurate start and ending values.

the graph that your function produces is an infinite curve ... they have no start or end to them.

anonymous · Answer

if you had to make an educated guess what would you pick because i need to pick something

amistre64 · Answer

2 things dictate the general shape of a polynomial:  the coefficient of the highest degree, and the highest degree itself

amistre64 · Answer

if i were to make a guess as to what in the world this question is talking about, id say that they assume that the domain and range of the graph is large enough, and that the 'parent' function is simply x^3.  if the left side where to be positive as x approaches negative infinity, then the function would have to be adjusted as -x^3  so the sign of the leading coeff.

anonymous · Answer

okay thank you again

amistre64 · Answer

good luck

anonymous · Answer

thanks