Question

Suppose a continuous function f(x) satisfies f(-3) = -4 and f(2) = 5. What does the IVT conclude?

A.There is a zero on the interval [-4, 5].
B.There is only one zero on the interval (-3, 2).
C.There is at least one zero on the interval (-4, 5).
D.There is at least one zero on the interval (-3, 2).

Answer 1

Do you know what IVT says?

Answer 2

yes

Answer 3

intermediate value theorem

Answer 4

I mean, do you know what that theorem states?

Answer 5

yes

Answer 6

Yes, it says this:

The intermediate value theorem states the following: If f is a real-valued continuous function on the interval [a, b], and u is a number between f(a) and f(b), then there is a c ∈ [a, b] such that f(c) = u.

Answer 7

yes

Answer 8

Alright, so this problem is pretty much asking you to interpret this theorem. How many values does it prove exist? One? Multiple?

Is it an interval on the x axis or the y axis

Answer 9

ohh ok

Answer 10

Aha moment? Note that the theorem doesn't tell you exactly how many zeroes there are - it just tells you there is at least one.

It could be a crazy function that curves up and down multiple times, for instance.

Answer 11

okay

Answer 12

So, do you think you can pick out the correct answer now? And understand why its right?

Answer 13

yes

Answer 14

Great - glad I could help.