(a) On what interval(s) is f increasing? (Select all that apply.) (- ? , -1 ) (-

Question

(a) On what interval(s) is f increasing? (Select all that apply.) (-?, -1)(-?, 0), (-?, 1), (-1, 1), (-1, ?), (0, 1), (0, ?), (-3, ?), None of these (-?, -1)(-?, 0), (-?, 1), (-1, 1), (-1, ?), (0, 1), (0, ?), (-3, ?), None of these (-?, -1)(-?, 0), (-?, 1), (-1, 1), (-1, ?), (0, 1), (0, ?), (-3, ?), None of these (-?, -1)(-?, 0), (-?, 1), (-1, 1), (-1, ?), (0, 1), (0, ?), (-3, ?), None of these
On what interval(s) is f decreasing? (Select all that apply.) (-?, ?), (-?, 0), (-?, 1), (-1, 3), (-1, 1), (0, 1), (-1, ?), (0, ?), (1, ?), none of these
(-?, ?), (-?, 0), (-?, 1), (-1, 3), (-1, 1), (0, 1), (-1, ?), (0, ?), (1, ?), none of these
(b) What are the local maximum value(s) of f? (Select all that apply.) (b) What are the local maximum value(s) of f? (Select all that apply.) -1, 0, 1/4, 1/2, 1, none of these
What are the local minimum value(s) of f? (Select all that apply.)
-1, 0, 1/4, 1/2, 1, none of these
(c) On what interval(s) is f concave upward? (Select all that apply.) (-?, 0), (-?, 2), (-?, -1), (-1, 1), (-1, 2), (0, ?), (-1, ?), (2, ?), none of these
On what interval(s) is f concave downward? (Select all that apply.)
(-?, 0), (-?, 2), (-?, -1), (-1, 2), (0, ?), (1, ?), (-1, ?), none of these
What are the x-coordinate(s) of the inflection point(s) of f? (Select all that apply.) -2, -1, 0, 1, 2, none of these On what interval(s) is f increasing? (Select all that apply.) (-?, -1)(-?, 0), (-?, 1), (-1, 1), (-1, ?), (0, 1), (0, ?), (-3, ?), None of these On what interval(s) is f decreasing? (Select all that apply.) (-?, ?), (-?, 0), (-?, 1), (-1, 3), (-1, 1), (0, 1), (-1, ?), (0, ?), (1, ?), none of these What are the local maximum value(s) of f? (Select all that apply.) -1, 0, 1/4, 1/2, 1, none of these What are the local minimum value(s) of f? (Select all that apply.) -1, 0, 1/4, 1/2, 1, none of these On what interval(s) is f concave upward? (Select all that apply.) (-?, 0), (-?, 2), (-?, -1), (-1, 1), (-1, 2), (0, ?), (-1, ?), (2, ?), none of these On what interval(s) is f concave downward? (Select all that apply.) (-?, 0), (-?, 2), (-?, -1), (-1, 2), (0, ?), (1, ?), (-1, ?), none of these What are the x-coordinate(s) of the inflection point(s) of f? (Select all that apply.) -2, -1, 0, 1, 2, none of these f (x) = x2/x2 + 3

Explanation / Answer

a)

increasing on (0, infy)

decreasing on (-inf, 0)

b)

f'(x) = 6x/(x^2+3)^2

f'(x) = 0

6x = 0

so,

x = 0 --critical number

f''(x) = -18(x^2 - 1)/(x^2+3)^3

put x = 0

f''(0) = -18( - 1)/(+3)^3 = 2/3 >0

so, local minimum at x = 0

and no local maximum.

i)

option : none of these

ii)

option: 0

c)

i)

concave up on

(-1, 1)

ii)

concave down on

(-inf, -1)

and

(1, +infy)

d)

x-coordinates: -1, 1

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