Suppose the function g(x) has a domain of all real numbers except x = 1. The sec

ID: 2854070 • Letter: S

Question

Suppose the function g(x) has a domain of all real numbers except x = 1. The second derivative of g(x) is shown below.

g''(x)=((x-5)(x+4))/(x+1)^3

(a) Give the intervals where g(x) is concave down. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

(b) Give the intervals where g(x) is concave up. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

(c) Find the x-coordinates of the inflection points for g(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

a) function is concave down ==> g ''(x) < 0

==> [(x-5)(x+4)]/(x+1)3 < 0

==> x belongs to (-, -4) U (-1 , 5)

b) function is concave up ==> g ''(x) > 0

==> [(x-5)(x+4)]/(x+1)3 > 0

==> x belongs to (-4 , -1) U (5 ,)

c) inflection points ==> g ''(x) = 0

==> x = 5 , -4

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