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## Homework Statement

Given the function f(x) = x^2*e^-x, x

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a)

Show that f'(x) = 2xe^-x - x^2 * e^-x

b)

we're going to examine the properties of the function f.

1: find the limits when x -> ∞

2: find potential global and local max/min.

3: draw the graph (this is pretty self explanatory and I'll most likely be able to do this without any problems, I'll just add it to get the complete exercise.)

c)

The line l tangents the graph to the function f at point given at x = 1.

Find the equation to the line and show that the line crosses the graph to x at origin.

d)

Find the area (flat(?)) defined by the graph to f(x) and the line y = e^-1 * x by calculations.

## Homework Equations

I'm currently at part a) where I'm struggling with the - sign in front of x^2 * e^-x.

## The Attempt at a Solution

f(x) = x^2 e^-x = u*v = u'v+uv'

u = x^2 u' = 2x

v = e^-x v = e^-x

f'(x) = 2x*e^-x + x^2 * e^-x

Why am I getting + instead of -? Does it have anything to do with the x

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Thanks for any input.