If f(x) has one or more local minima or minima, each occurs singly between adjacent roots of f(x) (figure d, below).

f (x)

f (x)

x

x

a

b

f (x)

f (x)

x

 

 

x

 

 

 

 

 

 

c

d

Function Whose Roots Can Be Found

In most situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x) = 0. However, a very small non–zero value for f(x) is often acceptable because it might result from approximating numbers with limited (12–digit) precision.

D-2More about Solving