Question For this problem, consider the function

y=f(x)=x^1/3(x²7²)

on the domain of all real numbers.(a) The value of

lim_xf(x)

is

. (If you need to use -or, enter -infinity or infinity.)

(b) The value of

lim_xf(x)

is

. (If you need to use -or, enter -infinity or infinity.)

(c) There are threex-intercepts; list these in increasing order: s=

, t=

, u=

.

(d) The intercepts in part (c) divide the number line into four intervals. From left to right, indicate the sign of the function on each of these intervals by typing "P" (for positive) or "N" (for negative):

sign on (,s)=

,

sign on (s,t)=

,

sign on (t,u)=

,

sign on (u,)

.

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

(f) There are three critical numbers for f(x); list these in increasing order:

v=

,

w=

,

z=

.

(g) The critical numbers in (f) break the domain into four intervals; on each, determine if the function is increasing or decreasing by typing "I" or "D":

sign on (,v)=

,

sign on (v,w)=

,

sign on (w,z)=

,

sign on (z,)

.

(h) There is a local minimum for f(x) occurring at x=

.

(i) There is a local maximum for f(x) occurring at x=

.

(j)lim_x0f'(x)=

. (If you need to use -or, enter -infinity or infinity; if the limit does not exist, write "DNE".)

T or F: There is a vertical tangent line at (0,0) on the graph

TrueFalse

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

(l) There is one inflection point (

,

) on the graph of f(x).

(m) T or F: The function is concave up atx=1? (Enter T or F.)

TrueFalse

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

ABCD