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Where would #f(x)= -14x^3 + 19x^3 - x - 2# have an inflection point?

Answer 1

Emma Aldridge

First of all I think there is a mistake in your writing, the second term I suppose it would be #19x^2#.

This is a cubic function, and the only zero of the second derivative is always the inflection point.

#y'=-42x^2+38x-1#

and

#y''=-84x+38# that is zero in #x=38/84=19/42#.

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Answer 2

Christopher Agresta

To find the inflection point of ( f(x) = -14x^3 + 19x^3 - x - 2 ), you need to find the points where the second derivative changes sign. Calculate the second derivative, set it equal to zero, and solve for ( x ). Then, check the concavity of ( f(x) ) around those points to confirm the inflection point.

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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.