​ f(x)=e^x/x^4 find intervals...

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

Correction to my previous answer.....it's only concave up  on   (0, inf)

The graph is never concave down....thus....no inflection point exists