Roots of Functions. The following problems relate to finding real roots for functionsIn th...

Roots of Functions. The following problems relate to finding real roots for functions

In the program developed in Section, we searched for subintervals for which the function values at the endpoints had different signs; we then estimated the root location to be the midpoint of the subinterval. A more accurate estimate of the root location is usually the intersection of a straight line through the function values with the x-axis, as shown in Figure.

Figure Straight line intersection in (a, b).

Using similar triangles, it can be shown that the intersection point c can be computed using the following equation:

Modify program chapter to estimate the root of a subinterval using this approximation.