A student uses the method of successive approximations to estimate a positive solution of f(x) = g(x), where f(x) = x2 + 10 and g(x) = 2x + 17. The table shows her results for different input values of x. x f(x) g(x) 0 10 17 1 11 19 2 14 21 3 19 23 4 26 25 3.5 22.25 24 Using this method, the next number selected should be between and .

The next number selected should be between 2 and 3 .

Step-by-step explanation:

x. x    f(x)             g(x)

0        10               17

1           11              19

2          14              21

3          19              23

4         26             25

3.5      22.25        24

2.5      16.25         22

1.5       12.25        20

0.5       10.25       18

We see the pattern that it is increasing with only a unit. The last given data is mid of the last two values that is 3 and 4.

So the next value would be the mid of the next last two values that is 2 and 3 and will be 2.5

Now it is moving in the reverse direction in the same pattern  with a difference of a unit.

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step-by-step explanation: