GROVE HSC 3U - TEST YOURSELF 9 (APPROX OF ROOTS) - Q6

It's up to you to find to values of $x$ such that the function value changes sign. 
It will be easy trial and error. (unlikely in an actual test)

Let's randomly (with a bit of intuition) try $x=0$ and $x=2$! 

$f(x)=x^3+3x-7$

$f(0)=-7<0$
$f(2)=2^3+3(2)-7=8+6-7=7>0$

Since $f(0)<0$ and $f(2)>0$, then there is at least one root  between $x=0$ and $x=2$.  

Now proceed to half the interval 3 times.....