Barrons AP Calculus - David Bock

number of subdivisions, and with L, R, M, and T denoting, respectively, left, right, midpoint, and

trapezoid sums, it follows that

(A) R ≤ T ≤ M ≤ L

(B) L ≤ T ≤ M ≤ R

(C) R ≤ M ≤ T ≤ L

(D) L ≤ M ≤ T ≤ R

(E) none of these

(A) + ∞

(B) 0

(C)

(D) −∞

(E) nonexistent

21. The only function that does not satisfy the Mean Value Theorem on the interval specified is

(A) f (x) = x^2 − 2x on [−3, 1]

(B)

(C)

(D)

(E)

22. Suppose f ′(x) = x(x − 2)^2 (x + 3). Which of the following is (are) true?
    I. f has a local maximum at x = −3.
    II. f has a local minimum at x = 0.
    III. f has neither a local maximum nor a local minimum at x = 2.
    (A) I only
    (B) II only
    (C) III only
    (D) I and II only
    (E) I, II, and III


23. If