We can write this as :
f(x) = e^x * x^-4
Take the frist derivative and set to 0
e^x * x^-4 + e^x * (-4 x^-5) = 0
e^x * x^-4 - 4 e^x * x^-5 = 0 factor
[e^x * x ^-5] [ x - 4 ] = 0
The first factor is never 0 ..... x - 4 = 0 means that we have a critical point at x = 4
Look at the graph : https://www.desmos.com/calculator/otj7wmmxcg
a) It increases from ( -inf , 0) and from (4, inf)
It decreases from ( 0, 4)
b) The graph is concave -up at all points where it exists
c) Since the graph never changes concavitiy....there is no inflection point