Question

Show that the equation x^3 + x -3 =0 has a solution between 1 and 2. That is the only information given

Answer 1

Answer:

Step-by-step explanation:

Given that:

$f(x) = x^3 + x - 3 = 0$

Since the given function is equal to zero, then the function :

$f(x) = x^3 + x - 3$

where;

$x = 1$ and

$x = 2$

$f(x) = (1)^3 + (1) - 3 \\ \\ f(x) = 1 + 1 - 3 \\ \\f(x) = -1 < 0$

$f(2) = x^3 + x - 3 \\ \\f(2) = (2)^3 + 3 - 3 \\ \\f(2) = 8 + 3 - 3 \\ \\f(2) = 11 - 3 \\ \\f(2) = 8 > 0$

Thus; f(1) < 0 and f(2) > 0