$Show\ that\ f(x)=x^3-5x+3$ $has\ a\ zero\ in\ each$ $of\ the\ intervals\ [-3,-2],\ [0,1]\ and\ [1,2].$
For example, $f(-3)= (-3)^3- 5(-3)+ 3= -27+ 15+ 3= -9< 0$ while $f(-2)= (-2)^3- 5(-2)+ 3= -8+ 10+ 3= 5> 0$.