# Maximum/Minimum-Check Please?

1. Jun 13, 2013

### Justabeginner

1. The problem statement, all variables and given/known data
Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].

2. Relevant equations

3. 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.

2. Jun 13, 2013

### Staff: Mentor

You don't "solve for zero", but I know what you mean - Set f' = 0 and solve that equation.
Your max and min look OK, but check this point (10, 100/(e^10) ).

3. Jun 13, 2013

### Justabeginner

Okay, I'll make sure. Thank you!

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