p(x) = a0 + a1 x + a2 x2 ... an xn
can be represented by the Scheme list
(a0 a1 a2 ... an)
For example the function p1, defined by
p1(x) = 4 + 3x + 5x2 is represented by the list
(4 3 5)
(1) Write a function eval_poly for which the application (eval_poly p v) evaluates a polynomial function represented as a Scheme list p with argument v For example:
(eval_poly '(1 2 3) 4)
evaluates to 57.
(2) The derivative of the polynomial function p for which
p(x) = a0 + a1 x a2 x2 ... ab xn
is the polynomial function p' for which
p'(x) = a1 + 2 a2 x2 + ... n an xn
Write a Scheme function derivative for which the call (derivative p)
converts a polynomial into its derivative.
For example (derivative '(3 4 5 6))
evaluates to (4 10 18).