**Example**: Use the Intermediate Value Theorem to show that the polynomial function

*f(x)= x^3 + 2x - 1*has a zero in the interval

*(0,1).*

**Solution**: Note that f is continuous on the closed interval

*(0,1).*Because

*f(0) = 0^3+2(0) -1 = -1*and

*f(1) = 1^3 +2(1) -1 =2*, it follows that

*f(0) < 0*and

*f(1) > 0*. You can then apply the Intermediate Value Theorem to conclude that there must be some

*c*in

*(0,1)*such that

*f(c)= 0*.

Source:

*Calculus of a Single Variable Sixth Edition*book