Process of finding a root to a function f(x) The value r is a root of f(x). The

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Process of finding a root to a function f(x)

The value r is a root of f(x). The value r is a root of f(x) if f(r) = 0and functions can have anywhere from no to infinite roots.

In calculus the intermidiate value theorem tells us that if a continuous function has a strictly positive value at one point (f(a) at some point x =a) and strictly negative value at some other point (f(b) at some other point x=b), then there must exist at least one point r trapped in the interval (a,b0 such that f(r) =0.

Solve the problem of finding a root r to a function f(x) given the trapping interval (a,b) and some level of allowable difference (a small number like 0.000001)

Step 1) Check the points a and b to see if they are the root (if yes, stop: return answer)

Step 2) Calculate the midpoint between a and b

step 3) Check the midpoint to see if it is the exact answer (iy yes stop: return midpoint)

Step 4) Check if the interval is too small (if yes, stop: return midpoint)

Step 4) if f(a) and f(midpoint) have opposite signs, then the root is trapped in the new interval (a,r). Repeat the algorithm with this new interval.

Step 5) The root must be trapped in the interval (r,b). Repeat the algorithm with this new interval.

Explanation / Answer

http://www.mathworks.in/matlabcentral/fileexchange/2181-numerical-methods-using-matlab-2e/content/edition2/matlab/chap_1/a1_2.m

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