**Exercise 1.40:** Define a procedure `cubic`

that can be used together with the `newtons-method`

procedure
in expressions of the form

```
(newtons-method (cubic a b c) 1)
```

to approximate zeros of the cubic x^{3} + ax^{2} + bx + c.

```
(define (cubic a b c)
(lambda (x)
(+
(* x x x)
(* a x x)
(* b x)
c)))
(define dx 0.00001)
(define (deriv g)
(lambda (x)
(/ (- (g (+ x dx)) (g x))
dx)))
(define (newton-transform g)
(lambda (x)
(- x
(/ (g x) ((deriv g) x)))))
(define (newtons-method g guess)
(fixed-point (newton-transform g) guess))
(define (fixed-point f first-guess)
(define tolerance 0.00001)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))
```

```
> (newtons-method (cubic -2 -9 18) -2)
2.000000000000876
> (newtons-method (cubic 8 3 6) 1)
-7.711875650348891
```

Note that Newton’s Method only finds a root not all roots or even all real roots.