;; Define the function f using the "func" command:
(func f(x) 5*cos(2*x)-2*x*sin(2*x))

;; Calculate f's derivative, and call it g:
(derfunc g f x)
(what g)

;; If we just ask for the roots of g, they may not be in the interval of interest:
(roots g 1)
(roots g 2)

;; Using bisection assures that our root is in the given interval...
(g 1)
(g 2)
;; the values differ in sign, so, since g is continuous, there's a root!
(bisection (function g) 1 2)

;; now let's find a root of the derivative on the interval [1,2]:
(def root (roots g 1))
root
(g root)

;; our minimum value....
(f root)

(def xvals (rseq 1 2 100))
(xgobips "ex4.ps"
   1  ;; red   level 
   0  ;; green
   0  ;; blue
   xvals 
   (f xvals)
   :x-axis t
   :morelines (list
	       (list 0 0 1 
		     xvals 
		     (g xvals)
		     "lndashed"
		     )
	       )
   :xtics (rseq 1 2 5)
   :xmin 1
   :xmax 2
   :ymin -6
   :ymax 2
   )