;; Compute the derivative of a function in using numeric differentiation ;; --------------------------------------------------------------------------- ;; ;; Write a higher order function `(approx-der f h)` that uses the ;; symmetric difference quotient to find a numerical approximation ;; to the derivative of the function f ;; ;; Your scheme function should accept two parameters. ;; The first, f, is a function. ;; The second parameter, h, is used to approximate the derivative. ;; ;; The formula for the symmetric quotient method is this: ;; ;; f(t+h) - f(t-h) ;; f' = ------------------ ;; 2h ;; ;; Choosing a smaller value of h leads to a better approximation. ;; ;;;;;;;;;;; (define (approx-der f h) ;; This function should return another function that ;; computes the derivative, NOT 0. Delete the 0! 0 ) ;;;;;;;;;; ;; Tests ;; ----- ;; This portion of the file will test your implementation. ;; You can check that the output of the tests is correct by ;; running `make check` at the bash prompt. ;; (define (println x) (begin (display x) (newline))) ; Check der(x^2) = 2x (let ((f (lambda (x) (* x x))) (h 0.0001)) (begin (println (round ( (approx-der f h) 1))) ; Expect 2 (println (round ( (approx-der f h) 2))) ; Expect 4 (println (round ( (approx-der f h) -2))) ; Expect -4 (println (round ( (approx-der f h) 10))) ; Expect 20 ) ) ; Check der(10x+2x^2) = 10+4x (let ((f (lambda (x) (+ (* 10 x) (* 2 x x)))) (h 0.0001)) (begin (println (round ( (approx-der f h) 1))) ; Expect 14 (println (round ( (approx-der f h) 2))) ; Expect 18 (println (round ( (approx-der f h) -2))) ; Expect 2 (println (round ( (approx-der f h) 10))) ; Expect 50 ) )