Question

Given the function f(x) = x^4 - 2x^3 - 6x^2 + 3x +1, use intermediate theorem to decide which of the following intervals contains at least one zero. Select all that apply.

Answer 1

Answers:

First option: [-2,-1]

Second option: [-1,0]

Third option: [0,1]

Sixth option: [3,4]

Please, see the attached files.

Thanks.

Answer 2

1,2,3 and 6

Explanation:

Intermediate theorem is if a continuous function has values of opposite sign inside an interval, then it has a root in that interval. So if we put edges of internal instead of x into the functions:

First choice:

f(-2)=3

f(-1)=-5

Contains at least one zero.

Second choice:

f(-1)=-5

f(0)=1

Contains at least one zero.

Third choice:

f(0)=1

f(1)=-3

Contains at least one zero.

Fourth choice:

f(1)=-3

f(2)=-17

Does not contain any zero.

Fifth choice:

f(2)=-17

f(3)=-17

Does not contain any zero.

Sixth choice:

f(3)=-17

f(4)=45

Contains at least one zero.