Consider
f(x)=x2e−xf(x) = x^2 e^{-x}f(x)=x2e−x
defined for all real xxx.
Find every critical point of fff, classify each one with the second derivative test, and evaluate fff at the point that turns out to be a local maximum.
Which statement is completely correct?
Select all that apply.
x=0x = 0x=0 is a local minimum, x=2x = 2x=2 is a local maximum, and the maximum value is 4e−24e^{-2}4e−2.
x=0x = 0x=0 is a local maximum, x=2x = 2x=2 is a local minimum, and the minimum value is 4e−24e^{-2}4e−2.
The critical points are x=0x = 0x=0 and x=−2x = -2x=−2; x=0x = 0x=0 is a local minimum and x=−2x = -2x=−2 is a local maximum.
x=0x = 0x=0 is a local minimum, x=2x = 2x=2 is a local maximum, and the maximum value is 2e−22e^{-2}2e−2.