P2 Have a cover page, table of contents, and cite all sources. The average slope formula is: f(x2)...

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P2
Have a cover page, table of contents, and cite all sources.
The average slope formula is: f(x2) - f(x1) / x2 - x1
It tells us the average slope over the interval from x1 to x2.
Take the average slope of the function x^2 + 3x +1 over one unit intervals from 0 to 10.
Repeat for 2x^2 -2x +5.
Graph the numbers (slopes), and what type of function do you see?
a) f(x) = x^2 + 3x +1

x1 x2 f(x1) f(x2) [f(x2) - f(x1)]/(x2 - x1)
0 1 1 5 4
1 2 5 11 6
2 3 11 19 8
3 4 19 29 10
4 5 29 41 12
5 6 41 55 14
6 7 55 71 16
7 8 71 89 18
8 9 89 109 20
9 10 109 131 22
0
5
10
15
20
25
0 5 10

We see a linear function in this case.
) f(x) = 2x^2 -2x +5.

x1 x2 f(x1) f(x2)...

David · Accepted Answer

P2 
Have a cover page, table of contents, and cite all sources.
The average slope formula is: f(x2) - f(x1) / x2 - x1
It tells us the average slope over the interval from x1 to x2.
Take the average slope of the function x^2 + 3x +1 over one unit intervals from 0 to 10.
Repeat for 2x^2 -2x +5.
Graph the numbers (slopes), and what type of function do you see?
a) f(x) = x^2 + 3x +1 
 
x1 x2 f(x1) f(x2) [f(x2) - f(x1)]/(x2 - x1)
0 1 1 5 4
1 2 5 11 6
2 3 11 19 8
3 4 19 29 10
4 5 29 41 12
5 6 41 55 14
6 7 55 71 16
7 8 71 89 18
8 9 89 109 20
9 10 109 131 22
0
5
10
15
20
25
0 5 10
 
 
We see a linear function in this case.
b) f(x) = 2x^2 -2x +5.

P2 Have a cover page, table of contents, and cite all sources. The average slope formula is: f(x2) - f(x1) / x2 - x1 It tells us the average slope over the interval from x1 to x2. Take the average...

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