Question

For f (x) = x4 – 2x2 – 7, use the Intermediate Value Theorem to determine which interval Must contain a zero of f.

A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4

Answer 1

Calculate the values of f(x) at each pair of numbers. The answer will be the pair for which the value of f(x) changes sign.

f(0) = -7
f(1) = -8
f(2) = 16 - 8 -7 = +1
f(3) = 81 - 18 -7 = +56
f(4) = an even bigger positive number
etc.
Clearly the answer is C.