Question

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 .

Answer 1

The next number selected should be between 2 and 3 .

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.