Help with a calculus problem?

Question

What is/are the conditions of the intermediate value theorem, such that a number c exists where f(c)=ysubzero

A. f(x) is continous on the interval [a,b]
B. lim f(x)= ysubzero
x->c
C. ysubzero is a number between f(a) and f(b)
D. A and B

and another choice is E. A and C

Answer 1

E.

The "intermediate value theorem" sounds complicated but it's not.

Suppose you know that the temperature at 5am was 31° F, and that at noon it was 45°F.

Since you know for a fact that temperature can't go up instantaneously, you know that, at some point between 5am and noon, the temperature was exactly 40° F. Or any other temperature between 31° F and 45° F.

This doesn't mean that it might not have been 40° F more than once! It just means that you know that the temperature was exactly 40° F at least once sometime between 5am and noon.

That's all the intermediate value theorem says. "If you know the y-values of a function at two different points, and you know the function is continuous, then you know that the function will pass through every y-value between the ones that you know at least once between the x-values that you know."