Question

7. (a) Sketch a graph of a function f(x) that satisfies all of the following conditions.

i. f(2) = 3 and f(1) = −1

ii. lim x→−4 f(x) = −∞

iii. limx→∞ f(x) = 1

iv. lim x→−∞ f(x) = −2

v. lim x→−1+ f(x) = ∞

vi. lim x→−1− f(x) = −∞

vii. f 0 (x) > 0 on (−4, −3.5) ∪ (−2.5, −1.5) ∪ (1, 2) ∪ (2, ∞)

viii. f 0 (x) < 0 on (−∞, −4) ∪ (−3.5, −2.5) ∪ (−1.5, −1) ∪ (−1, 1)

ix. f 00(x) > 0 on (−3, −2) ∪ (−1, 2) x. f 00(x) < 0 on (−∞, −4) ∪ (−4, −3) ∪ (−2, −1) ∪ (2, ∞)

(b) Based on the function sketched in part (a), locate the x-coordinates of all discontinuities of f(x) and state their types.

Answer 1