Question For this problem, consider the function

y=f(x)= sqrt(|x|)+x/2

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 twox-intercepts; list these in increasing order: s=

, t=

.

(d) The intercepts in part (c) divide the number line into three 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,)

.

(e) If x is positive, the formula forf '(x)=

. If x is negative, the formula forf '(x)=

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

v=

,

w=

.

(g) The critical numbers in (f) break the domain into three 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,)

.

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

.

(i)lim_x0f'(x)=

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

(j) Whenxis positive, the formula forf ''(x)=

. Ifxis negative, the formula forf ''(x)=

.

(k) TRUE or FALSE: The function is concave up atx=1?

TrueFalse

(l) TRUE or FALSE: The function is concave up atx=-1?

TrueFalse

(m) TRUE or FALSE: There is an inflection point at (0,0) on the graph.

TrueFalse

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

ABCD