# How do you use the Intermediate Value Theorem to show that the polynomial function #F(x)=x^3+2x+1 # has a root in the interval [-2, 1]?

##### 1 Answer

Oct 16, 2015

You put the borders of the interval in the function.

#### Explanation:

Let's try to put the borders of the interval in the function:

Since you have one function value between that is negative and one that is positive and since the function is continuous in

You can easily see this if you plot the function:

graph{y=x^3+2x+1 [-3,2,-12,5]}

You can see that the function needs to go trough