Find Maximum and Minimum Values on Interval [-10, 10] for y= x^2(e^-x)

[Justabeginner]

Homework Statement

Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].

Homework Equations

The Attempt at a Solution

f'(x)= 2x*(e^(-x)) - (e^(-x)*(x^2))
f'(x)= x*e^(-x) (2- x)
Solve for zero, for critical points? I got two solutions: x=0 or x= 2

Plugging these two critical points and the endpoints on the interval back into f(x), I get:
(0, 0) - Minimum
(2, 4/(e^2) )
(-10, 100*(e^10) ) - Maximum
(10, 100/(e^10) )

Is this right? Thank you.

 

[Mark44]

Homework Statement

Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].

Homework Equations

The Attempt at a Solution

f'(x)= 2x*(e^(-x)) - (e^(-x)*(x^2))
f'(x)= x*e^(-x) (2- x)
Solve for zero, for critical points? I got two solutions: x=0 or x= 2

You don't "solve for zero", but I know what you mean - Set f' = 0 and solve that equation.

Plugging these two critical points and the endpoints on the interval back into f(x), I get:
(0, 0) - Minimum
(2, 4/(e^2) )
(-10, 100*(e^10) ) - Maximum
(10, 100/(e^10) )

Is this right? Thank you.

Your max and min look OK, but check this point (10, 100/(e^10) ).

 

[Justabeginner]

Okay, I'll make sure. Thank you!