Let f(x) = x³ + 2x - 2.

(a) Use the Intermediate Value Theorem (stated below) to show that the equation f(x) = 0

has a solution in the interval (-1,1). (In other words, f had a root strictly between

-1 and 1.)

(b) What property of this function f allows us to use the Intermediate Value Theorem?

(c) The Intermediate Value Theorem guarantees that the equation f(x) = 0 has at least one

solution in the interval (-1, 1). But in this case, it turns out that there is exactly one

solution. How can you show that there is exactly one solution using other techniques

from Calculus?