Question

Question For this problem, consider the function

y=f(x)=

|x|

+

x

3

on the domain of all real numbers.

(a) The value of

lim_{x→ ∞}f(x)

is

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

(b) The value of

lim_{x→ −∞}f(x)

is

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

(c) There are two x-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 for f '(x)=

. If x is negative, the formula for f '(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_{x→ 0}f '(x)

=

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

(j) When x is positive, the formula for f ''(x)=

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

.
(k) TRUE or FALSE: The function is concave up at x=1?

TrueFalse    

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

TrueFalse    

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

TrueFalse    

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

AB    CD

5. [-122 Points) DETAILS Question for this problem, consider the function y=f(x)=V]x] + on the domain of all real numbers. (a) The value of limx-f(x) is (If you need to use -- or -, enter infinity or infinity.) (b) The value of limx--- (x) is (If you need to use or o, enter infinity or infinity.) (c) There are two x-intercepts; list these in increasing order: s= (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 (-0,s) sign on (s,t)- sign on (t, . ) (e) If x is positive, the formula for f '(x)= . If x is negative, the formula for f '(x)= () There are two critical numbers for f(x); list these in increasing order: V= WE