Question For this problem, consider the function y= f(x)=x1/3(x2_42) on the domain of all real numbers. (a) The value of lim co f(x) (If you need to use -co or co, enter -infinity or infinity.) (b) The value of lim -co f(x) (If you need to use -co or a, enter -infinity or infinity.) (c) There are three x-intercepts; list these in increasing order: s= -4 4 (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 ( -00 ,s) = N sign on (s,t)= P sign on (t,u)= sign on (u, 0 ) P (e) What is the formula for f '(x)= 16 -() (f) There are three critical numbers for f(x); list these in increasing order: V= W= (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 ( -00 , V)= sign on (v,w) = sign on (w,z)= sign on (z, 00 )(h) There is a local minimum for f(x) occurring at x= (i) There is a local maximum for f(x) occurring at x= VT X (j) limx . of '(x) = 0 . (If you need to use -co or co, enter -infinity or infinity; if the limit does not exist, write "DNE".) X T or F: There is a vertical tangent line at (0,0) on the graph O True O False (28x2 + 32 (k) The formula for f "(x)= 3 (1) There is one inflection point (| 0 0 ) on the graph of f(x). (m) T or F: The function is concave up at x=1? (Enter T or F.) O True O False (n) The graph of y=f(x) is best represented by which of the following pictures (select A, B, C or D): OA OB OC OD PlotA PlotB At PlotC PlotD