(1 point) Answer the following questions for the function e2-4 defined on the in
ID: 2886718 • Letter: #
Question
(1 point) Answer the following questions for the function e2-4 defined on the interval [-16, 18 interval |-16, a.) Enter the r-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it, if there are more than one, enter them separated commas; and if there are none, enter NONE Answer. b.) f(z) is concave up on the region Note: Give your answer in interval notation c.) Enter the -coordinates of the inflection point(s) for this function as a comma-separated list Answer.Explanation / Answer
a)
To find vertical asymptote, set denominator =0 and then solve for x
x² -4 =0
(x+2)(x-2) =0
x= -2, 2
b)
y=x^3/(x²-4)
Find derivative using quotient rule as
f'(x) = (x^2 (x^2 - 12))/(x^2 - 4)^2
Find second derivative as
f"(x) =(8 x (x^2 + 12))/(x^2 - 4)^3
Now concave up means f"(x) is positive, hence in interval
(-2,0)U(2, infinity)
c)
To find inflection point, solve f"(x) =0
(8 x (x^2 + 12))/(x^2 - 4)^3 =0
(8 x (x^2 + 12)) =0
8x =0
x=0
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