Question

Evaluate f(x) = x3 - 9x at 2 and 4 to determine if the Intermediate Value Theorem guarantees that a zero exists between the two values.

a) f(2) =


b) f(4) =

Answer 1

Answer:

If f is continuous on a closed interval [a,b] and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that f(x) = c.

You function is:

f(x) = 4x5 -x3 - 3x2 + 1

It is continuous on the interval [-3,-1]. The value of c we want is c = 0, that is f(x) = 0. Compute f(-3) and f(-1).

f(-3) = 4(-3)5 - (-3)3 - 3(-3)2 + 1 = _____

f(-1) = 4(-1)5 - (-1)3 - 3(-1)2 + 1 = _____