Barrons AP Calculus - David Bock

FIGURE N2–12

EXAMPLE 31

Is continuous at x = 2?

SOLUTION: g(x) is not continuous at x = 2 since This discontinuity can be

removed by redefining g(2) to equal 4. See Figure N2–13.

FIGURE N2–13

THEOREMS ON CONTINUOUS FUNCTIONS
(1) The Extreme Value Theorem. If f is continuous on the closed interval [a,b], then f attains a
minimum value and a maximum value somewhere in that interval.
(2) The Intermediate Value Theorem. If f is continuous on the closed interval [a,b], and M is a
number such that f (a) ≤ M ≤ f (b), then there is at least one number, c, between a and b such that f (c)
= M.