For this problem, consider the function

y=f(x)=

x³

x² 1

(a) Theyintercept is the point (

,

).

(b) The onlyxintercept is atx=

.

(c) The left-most vertical asymptote has equationx=

.

(d) The right-most vertical asymptote has equationx=

.

(e) What is the formula forf'(x)=

(f) How many critical numbers are there forf(x)?

(g) There are three critical numberschaving the property thatf'(c)=0; list these in increasing order:

(h) The open intervals on whichf(x)is increasing. (Enter the interval that contains smaller numbers first. If you need to use -or, enter -infinity or infinity.)(,)

(,)

(i) The open intervals on whichf(x)is decreasing. (Enter the interval that contains smaller numbers first. (If you need to use -or, enter -infinity or infinity.)(,)

(,)

(,)

(j) There is a local maximum occurring atc=

.

(j) There is a local minimum occurring atc=

.

(k) The formula forf''(x)=

(l) The open intervals on whichf(x)is concave up. (Enter the interval that contains smaller numbers first. (If you need to use -or, enter -infinity or infinity.)(,)

(,)

(m) The open intervals on whichf(x)is concave down. (Enter the interval that contains smaller numbers first. If you need to use -or, enter -infinity or infinity.)(,)

(,)

(n) T or F: There is an inflection point at (-3,f(-3))

TrueFalse

.

(o) T or F: There is an inflection point at (0,f(0))

TrueFalse

.

(p) T or F: There is an inflection point at (3,f(3))

TrueFalse

.

(q) The graph ofy=f(x)is best represented by which of the following pictures (select A, B, C or D):

ABCD