For more information including compatibility, examples and test cases, see https://github.com/petercrlane/r7rslibs
0.1. Minimize: (import (slib minimize))
The Golden Section Search algorithm can find minima of functions where derivatives are expensive to compute or unavailable.
0.1.1. goldensectionsearch
goldensectionsearch
takes four arguments:

the function to minimize (of one argument)

the lowest value of
x
to search from 
the highest value of
x
to search to 
a stopping condition for the search, which is one of

a positive number defines a target tolerance

a negative number is negated to define the number of iterations

a function of
(x0 x1 a b fa fb count)
ends the search by returning#t

The function returns a dotted pair: the value of x
for the minimum and f(x)
sash[r7rs]> (goldensectionsearch square 10 10 100) ; <1> (4.258043576850981e21 . 1.8130935102361897e41) ; <2>

Find the minimum of the
square
value in range (10, 10) for 100 iterations 
The minimum is x=0 and (square x)=0
The following example minimizes its function to within the specified tolerance:
sash[r7rs]> (goldensectionsearch (lambda (x) (+ (* x x x) (* 2 x) 5)) 0 1 (/ 10000))) (0.8164883855245578 . 6.0886621077391165)
Further documentation: http://people.csail.mit.edu/jaffer/slib/Minimizing.html