# For what values of x is #f(x)=(2x^2−4x)e^x# concave or convex?

The function is convex for

Calculate the first and second derivatives

The roots are

We can build the variation chart

graph{(2x^2-4x)e^x [-17.35, 14.68, -7.95, 8.07]}

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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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- What are the local extrema and inflection points for #y = 2sin (x) - cos^2 (x)# for #[0, 2π]#?
- If #y=2x+tanx#, find #y'''# third derivative of #y#?

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