# For what values of x is #f(x)=(x^2−x)e^x# concave or convex?

The function is convex on

The function is concave on

First, find the second derivative.

First Derivative

Use product rule.

Second Derivative

Use product rule again.

graph{e^x(x^2-x) [-10, 10, -5, 5]}

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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