Which one of the following facts is NOT needed to use the Intermediate Value Theorem to prove that f(x)=x^4-3x^3-7 has a root c between x = 3 and x = 4?

**Answer:**

At x=3

F(3)=3^4-3 . 3^3-7= -7

At x=4

F(4)=4^4-3 . 4^3-7=57

Now we know:

at x=3, the curve is below zero

at x=4, the curve is above zero

And, being a polynomial, the curve will be continuous,

so somewhere in between, the curve must cross through y=0

Yes, there is a solution to f(x)=x^4-3x^3-7 in the interval [3, 4]