intermediate value theorem

[alyren]

use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

F(x)=3x^3+10x+2; [-1,0]

so far i got
F(-1)=3(-1)^3+10(-1)+2
F(-1)=-11

F(0)=3(0)^3+10(0)+2
F(0)=2

and i dont know the rest what to do.

 

[wjm11]

use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

F(x)=3x^3+10x+2; [-1,0]

so far i got
F(-1)=3(-1)^3+10(-1)+2
F(-1)=-11

F(0)=3(0)^3+10(0)+2
F(0)=2

Plot these two points on a graph. One is above the x-axis, and the other is below.

If the function is continuous over the stated interval, then the function must cross the x-axis at some point (to get from one plotted point to the other). Make sense?

That means there is a "zero" on this interval.