10

True/False and Multiple Choice Questions

SECTION 4.5 1. f (x) = 3x2 − 4x + 2 has an absolute maximum on [−2, 2] of A. 16

B. 22

C. 12

D. 4.

C. 1

D. 5.

2. f (x) = |5 − 2x| has an absolute minimum of A. 0

B. 3

3. Answer true or false. f (x) = x3 − x2 + 2 has an absolute maximum and an absolute minimum. 4. Answer true or false. f (x) = x3 − 18x2 + 20x + 2 restricted to a domain of [0, 20] has an absolute maximum at x = 2 of −22, and an absolute minimum at x = 10 of −598. 5. f (x) =

√

x − 2 has an absolute minimum of

A. 0 at x = 2 6. f (x) =

√

B. 0 at x = 0

C. −2 at x = 0

D. 0 at x = −2.

x2 + 5 has an absolute maximum, if one exists, at

A. x = −5

B. x = 5

C. x = 0

7. Find the location of the absolute maximum of tan x on [0, π], if it exists. π A. 0 B. π C. 2

D. None exist.

D. None exist.

8. f (x) = x2 − 3x + 2 on (−∞, ∞) has A. B. C. D.

only an absolute maximum only an absolute minimum both an absolute maximum and an absolute minimum neither an absolute maximum nor an absolute minimum. 1 on [1, 3] has x2 an absolute maximum at x = 1 and an absolute minimum at x = 3 an absolute minimum at x = 1 and an absolute maximum at x = 3 no absolute extrema an absolute minimum at x = 2 and absolute maxima at x = 1 and x = 3.

9. f (x) = A. B. C. D.

10. Answer true or false. f (x) = sin x cos x on [0, π] has an absolute maximum at x =

π . 2

11. Use a graphing utility to assist in determining the location of the absolute maximum of f (x) = −(x2 − 3)2 on (−∞, ∞), if it exists. √ √ √ A. x = 3 and x = − 3 B. x = 3 only C. x = 0 D. None exist. 12. Answer true or false. If f (x) has an absolute minimum at x = 2, −f (x) also has an absolute minimum at x = 2. 13. Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is deﬁned on an interval [−a, a], where a is ﬁnite.

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