Can someone help me out with this?
Given the function f(x)=x^4+3x^3-2x^2-6x-1, use the Intermediate Value Theorem to decide which of the following intervals contains at least one zero. Select all 4 that apply.
a. [-4,-3]
b. [-3,-2]
c. [-2,-1]
d. [-1,0]
e.[0,1]
f.[1,2]

Question

Can someone help me out with this?
Given the function f(x)=x^4+3x^3-2x^2-6x-1, use the Intermediate Value Theorem to decide which of the following intervals contains at least one zero.  Select all 4 that apply.
a. [-4,-3]
b. [-3,-2]
c. [-2,-1]
d. [-1,0]
e.[0,1]
f.[1,2]

eliesaab · Answer

f(-4)=55
h(3)=125
a) is not a choice. Why?

eliesaab · Answer

h[0]=-1
h(1)=-5
e) is not a choice.
What is left?

eliesaab · Answer

replace h by f in the above post

eliesaab · Answer

To have a root in the interval [a,b] f(a) and f(b) must be of different sign. Meaning that if one them is positive the other must be negative

eliesaab · Answer

Are you with me?

jadareese_18 · Answer

Yes, I'm following what you're saying.

eliesaab · Answer

2 out of the 6 available options are ruled out, so the 4 remaining must work according to the question

eliesaab · Answer

You can try them and see that each one fo them work

jadareese_18 · Answer

Alright thank you very much.  You really helped me figure out how to understand this problem. @eliesaab

eliesaab · Answer

YW

jadareese_18 · Answer

Yes, I checked them and they were correct.

eliesaab · Answer

Great