# How do you determine the interval(s) on which the function #y= ln(x) / x^3# is concave up and concave down?

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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.

- What are the points of inflection, if any, of #f(x)=12x^3 -16x^2 +x +7 #?
- For what values of x is #f(x)=(2x-2)(x-3)(x+3)# concave or convex?
- How do you sketch the curve #f(x)=e^x/(1+e^x)# ?
- How do you graph the function #y=5x-x^2#?
- How many points of inflection does the function #f(x) = (pi/3)^((x^3)-8)# have?

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