Answer:
- <u><em>The positive solution to the nearest tenth is (2.4, - 0.2).</em></u>
Explanation:
I will rewrite the table to understand how the <em>process of solving using succesive approximations</em> is.
<u>Table:</u>
x f(x) g(x)
0 - 5 - 6
1 - 3 - 5
2 - 1 - 2
3 1 3
Those are the points shown in the table.
Now you must continue the <em>process of solving using successive approximations</em> until you find the positive solution to the nearest tenth.
You need to determine whether a "guess" is closer or farther away of the solution.
The first row shows that g(x) is less than f(x) in 1 unit when x = 0 ( -6 - (-5) ) = -1.
The second raw shows that g(x) is less than g(x) in 2 units when x = 1 ( - 5 - (-3) ) = - 2
The third row shows that g(x) is is less than f(x) in 1 unit when x = 2 ( - 2 - (-1) ) = - 1.
The fourth row shows that g(x) is than f(x) in 2 units when x = 3 ( 3 - 1 = 2).
Hence, the trend changed form negative to positive, meaning that, since the functions are continous, there must be an intertemediate value of x (between x = 2 and x = 3) for which f(x) = g(x) and that is the solution.
Therefore, test x = 2.5
- f(x) = 2x - 5 = 2(2.5) - 5 = 0
- g(x) = x² - 6 = (2.5)² - 6 = 0.25
- g(x) - f(x) = 0.25 Thus the difference is bigger than one tenth (0.1)
Test for x = 2.4
- f(2.4) = 2(2.4) - 5 = - 0.2
- g(2.4) = 2.4² - 6 = -0.24
- g(2.4) - f(2.4) = - 0.24 - (0.2) = -0.04
Now the difference is less than 0.1 and the solution to the nearest tenth is (2.4, - 0.2).