# For what values of x is #f(x)=(-2x)/(x-1)# concave or convex?

Study the sign of the 2nd derivative.

For

For

You need to study curvature by finding the 2nd derivative.

The 1st derivative:

The 2nd derivative:

Here is a graph so you can see with your eyes:

graph{(-2x)/(x-1) [-14.08, 17.95, -7.36, 8.66]}

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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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- How do you find the inflection points for the function #f(x)=e^(3x)+e^(-2x)#?

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