Answer:
Step-by-step explanation:
Given is a function f(x)
[tex]f(x) = x^2 e^{-x}[/tex]
We have to analyse and sketch the grapy
X intercept : Put y =0, we get x =0 or infinity
Y intercept: Put x =0 , we get y =0
The function being product of a square divided by power of e can never be negative. Hence range is (0,infty)
Since when y=0 x has a solution as infinity, x axis is asymptote
[tex]f'(x) = (2x -x^2)e^{-x}[/tex]
f' becomes 0 when x = 0 or 2
[tex]f''(x) = (-2x +x^2+2-2x)e^{-x}[/tex]
f"(x) >0 for x=2 and <0 for x=0
Hence maxima at x=2 and minima at x=0
Graph is attached below
