Question

How do you find the local extrema for `(x^2)(e^-x)` from [-2,4]?

Answer 1

`PMIN[0,0],PMAX[-2,4e^2]`

Explanation:

We get
`f'(x)=e^(-x)(2x-x^2)`
`f''(x)=e^(-x)(x^2-4x+2)`
solving

`f'(x)=0`
we get
`x=0`
`f''(0)>0`
`x=2`
`f''(2)=e^(-2)(-2)<0`

since

`f(-2)=4e^2>4e^(-2)`

we get the Points as above.