# How do you use the intermediate value theorem to explain why #f(x)=x^3+3x-2# has a zero in the interval [0,1]?

##### 1 Answer

Nov 19, 2016

therefore

#### Explanation:

The intermediate value says:

If

#f(x)# is a continuous function over the domain#x in [a,b]#

then for any value#k in [f(a),f(b)]#

there is a value#c# such that#f(c)=k#

For the given function

Since

there is a value

[Technically, I have assumed without proof that