Answer:
c. x about 57/16
Explanation:
You have not specified the algorithm you use for one iteration. We will define it as follows:
The starting point is a pair of numbers that are upper and lower bounds on the solution. The iteration ends when a new value replaces one of these bounds. The final estimate of the root will be the average of the latest upper and lower bounds.
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The given graph shows suitable initial bounds are 3 and 4. The sign of h(x) = f(x)-g(x) matches the sign of h(3) when x=7/2, so the value 7/2 will replace the lower bound at the end of iteration 1.
The new average of upper and lower bounds is (7/2 +4)/2 = 15/4. The sign of h(15/4) matches the sign of h(4), so 15/4 becomes the new upper bound at the end of iteration 2.
The new average of the bounds is (7/2 +15/4)/2 = 29/8. The sign of h(29/8) matches the sign of h(15/4), so 29/8 becomes the new upper bound at the end of iteration 3.
After 3 iterations, the bounds are 7/2 and 29/8. The average of these values is the approximate solution to the equation:
x = (7/2 +29/8)/2 = 57/16
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Additional comment
We have tried to be clear about what we consider to be one iteration, and how a root approximation is arrived at. The definition of these things provided by your curriculum materials may be different.