# How do you know where the graph of f(x) is concave up and where it is concave down for #f(x) = x^3 + x#?

The graph of

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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.

- How do you graph #f(x)=x^3-3x^2-9x+6# using the information given by the first derivative?
- What are the points of inflection, if any, of #f(x)=x^4-x^3+6 #?
- What is different between critical point and inflection point?
- How do you find the first and second derivative of #(ln(x^2-1))/x^2#?
- Is #f(x)=e^(3-3x)+x/ln2x# concave or convex at #x=1#?

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