# Is #f(x)=(x-2)e^x # increasing or decreasing at #x=-2 #?

decreasing.

You need to remember these rules:

Applying this rule gives us:

A graph always helps to visualise and confirm these solutions: graph{(x-2)e^x [-10.114, 7.666, -4.41, 4.48]}

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To determine if ( f(x) = (x - 2)e^x ) is increasing or decreasing at ( x = -2 ), we need to evaluate the sign of the derivative at that point.

First, find the derivative of ( f(x) ): [ f'(x) = e^x(x - 1) ]

Now evaluate ( f'(-2) ): [ f'(-2) = e^{-2}(-2 - 1) = -\frac{3}{e^2} ]

Since ( f'(-2) ) is negative, ( f(x) ) is decreasing at ( x = -2 ).

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