Question

Let f(x) = xcubed + x-1
(i) Use the Intermediate Value Theorem to show that f (x) has at least one root in the interval
[0, 1].
(ii) Starting at x0=1, use the Newtons method to approximate this root.

Answer 1

f(x)= x³ +x-1

f(x)= 0, (0, 1)

f(0)= (0)³+(0)- 1

= -1

f(1)= (1)³+ (1)-1

=1