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

Answer 1

Christopher Allers

(5,15)

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

#y=x^3-15x^2+33x+100#

#y'=3x^2-30x+33#

#y''=6x-30#

#6x=30#

#x=5#

Now that you have your #x#, plug it into your first equation:

#y(5)=(5)^3-15(5)^2+33(5)+100# #=125-375+165+100=15# The inflection point is (5,15)

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Answer 2

Isaiah Allen

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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Answer from HIX Tutor

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.