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

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

In the program developed in Section 4.8 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. Using similar triangles, it can be shown that the intersection point c can be computed using the equation

Modify program chapter4_7 to estimate the root of a subinterval using this approximation.

Figure Straight line intersection in (a,b).