# How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = 10x^4 - 2x^2 + 7x - 1# has a root in the interval [-3, 0]?

##### 1 Answer

See the explanation.

#### Explanation:

The Intermediate Value Theorem says that

if

In general, to show that a function attains a chosen value, call it

Show that the function is continuous on

Show that

Conclude, using the Intermediate Value Theorem, that there is a

In this case,

Therefore, by the Intermediate Value Theorem, there is a

This

**Final Note** In mathematics "there is a" mean "there is at least one". It does NOT mean "there is exactly one".

.