# What are the coordinates of the point of inflection on the graph of #y=x^3-15x^2+33x+100#?

(5,15)

You must take the second derivative in order to determine the inflection point.

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To find the coordinates of the point of inflection on the graph of (y = x^3 - 15x^2 + 33x + 100), you need to find the second derivative of the function and then determine where it equals zero. The second derivative of the given function is (y'' = 6x - 30). Setting this equal to zero and solving for (x), we get (6x - 30 = 0), which yields (x = 5).

To find the corresponding (y)-coordinate, substitute (x = 5) into the original function: (y = (5)^3 - 15(5)^2 + 33(5) + 100 = 25 - 375 + 165 + 100 = -85).

So, the coordinates of the point of inflection are ((5, -85)).

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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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