SOLUTION: 11- Show work, for the function f(x)=x³+x, find the average rate of change of f from 1 to x: a- x³+x+2 x-1 b- x²+x+2 c- x²+2 d- 1

Algebra ->  Functions -> SOLUTION: 11- Show work, for the function f(x)=x³+x, find the average rate of change of f from 1 to x: a- x³+x+2 x-1 b- x²+x+2 c- x²+2 d- 1       Log On


   

Question 666619: 11- Show work, for the function f(x)=x³+x, find the average rate of change of f from 1 to x:
a- x³+x+2
x-1
b- x²+x+2
c- x²+2
d- 1
Found 2 solutions by swincher4391, ewatrrr:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Average rate of change from a to b of f(x): %28f%28b%29-f%28a%29%29%2F%28b-a%29
%28f%28x%29+-+f%281%29%29%2F%28x-1%29+=+%28x%5E3+%2B+x+-+2%29%2F%28x-1%29
Use long division to arrive at the result:
x-1 | x^3+x-2
x goes into x^3 x^2 times
(x-1)x^2 = x^3 - x^2
x^2+x-2 is what's left.
x-1 | x^2 +x -2
x goes into x^2 x times

(x-1) * x = x^2-x
2x -2 is whats left.
x goes into 2x 2 times.
2*(x-1) = 2x-2
So there's nothing left (remainder of 0)
giving us x^2+x+2

x^2+x+2. Choice B

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

f(x)=x³+x, find the average rate of change of f from 1 to x: 

f(x) - f(1)/(x-1) = 

Note:x^3 + x - 2 ,  x = 1 a root 0r (x-1) a factor 

using Synthetic Divsion

1	1	0	1	-2

 	 	1	1	2

 	1	1	2	0

generates the factor

  x^2 + x + 2