Home > Calculus > Determining Points of Inflection for a Function

What is the x-coordinate of the point of inflection on the graph of #y = (1/3)x^3 + 5x^2+ 24#?

Answer 1

Elijah Abram

#-5#

#y = (1/3)x^3 + 5x^2+ 24#

#y' = x^2 + 10x#

#y'' = 2x + 10#, which is #0# at #x=-5#

The only place that the graph might change concavity is at the point where #x=-5#

If you check, you'll find that #y''# is negative for #x<-5# and positive for #x> -5#. So the concavity changes at #(-5, 322/3)#

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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.

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