# Math Help - Continuous Functions

1. ## Continuous Functions

I'm having trouble with this question. I think we have to use the intermediate value theorem for this question.

$Show\ that\ f(x)=x^3-5x+3$ $has\ a\ zero\ in\ each$ $of\ the\ intervals\ [-3,-2],\ [0,1]\ and\ [1,2].$

2. Use the "intermediate value property"- if f is a continuous function and f(a)< f(b), then, for x between a and b, f(x) takes on every value between f(a) and f(b).

For example, $f(-3)= (-3)^3- 5(-3)+ 3= -27+ 15+ 3= -9< 0$ while $f(-2)= (-2)^3- 5(-2)+ 3= -8+ 10+ 3= 5> 0$.