For the first one

dy/dx = 4(x+1)^3 e^(-x ) -(x+1)^4e^(-x)

= e^(-x)*(x+1)^3[ 3-x]

the zeroes are x =-1 and 3

Use either a graph or test pts to determine sign on intervals (-inf,-1)

(-1,3) and (3,inf)

Remember any exponential is always positve so you can simplify

by considering (x+1)^3[ 3-x] only

In part 2 it works the same except you also have to consider the second derivative as well