# How do you use the intermediate value theorem to verify that there is a zero in the interval [0,1] for f(x)=x^3+3x-2?

Nov 5, 2016

See the explanation below

#### Explanation:

The intermediate value theorem states that if $f \left(x\right)$ is continuous on a closed interval $\left(a , b\right)$, and $c$ is a number such that $f \left(a\right) \le c \le f \left(b\right)$, then there is a number $x$ in the closed interval such that $f \left(x\right) = c$.
Here, $f \left(x\right)$ is a polynomial function continous on the interval $\left(0 , 1\right)$
such that $f \left(0\right) = 0 + 0 - 2 = - 2$ and $f \left(1\right) = 1 + 3 - 2 = 2$

Then there exists $0$ such that $f \left(0\right) < 0 < f \left(1\right)$

There exists x∈(0,1) such that $f \left(x\right) = 0$