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Mathematics 58 Online
OpenStudy (anonymous):

how do I find point of inflection of any function such as y=3x^2+2x+1

terenzreignz (terenzreignz):

Hiya :) A point of inflection is a point where it suddenly changes from a concave upward curve to a concave downward curve, or vice versa.

terenzreignz (terenzreignz):

But that doesn't really help us much, does it? :D Here's a tip... POSSIBLE points of inflection are points where the second derivative is zero...

OpenStudy (anonymous):

Is it really zero at second derivative? I didnt know that

terenzreignz (terenzreignz):

No... But what I'm saying is... only points where the second derivative is zero could POSSIBLY be points of inflection. Now, what's the second derivative of this function?

OpenStudy (anonymous):

If i have to find answer for the function i wrote in question, how would u do that Can u show me one example

terenzreignz (terenzreignz):

Well, let's take the function x^3... It's second derivative is 6x, right?

OpenStudy (anonymous):

yes

terenzreignz (terenzreignz):

When is 6x = 0?

OpenStudy (anonymous):

x=0

terenzreignz (terenzreignz):

That's right. And no others, right?

OpenStudy (anonymous):

no

terenzreignz (terenzreignz):

Okay, so x=0 (and y=0, since y = x^3) is a POSSIBLE point of inflection. In fact, it IS a point of inflection, but more on that later. Now, back to your function, what is it second derivative?

OpenStudy (anonymous):

6

terenzreignz (terenzreignz):

Yeap :) Now ask yourself, when is this equal to zero?

OpenStudy (anonymous):

no where

OpenStudy (anonymous):

so no point of inflection right? :D

OpenStudy (amistre64):

critical points are at 0 OR undefined.

terenzreignz (terenzreignz):

That's right :) that means there are no POSSIBLE points of inflection, and therefore, no point of inflection. Makes sense, right? This has a graph in the shape of a parabola, which has a consistent concavity, be it upwards or downwards (upwards in this case) And in both cases, the concavity doesn't change... at all :)

OpenStudy (anonymous):

okay that helps thank you :)

terenzreignz (terenzreignz):

No problem :)

OpenStudy (anonymous):

so mostly its gonna be for function whose exponents are > or = 3

terenzreignz (terenzreignz):

Or functions which aren't polynomials at all ;)

terenzreignz (terenzreignz):

Like the sine function... it has (infinitely) many points of inflection :D

OpenStudy (anonymous):

yeah right

terenzreignz (terenzreignz):

^sounds sarcastic XD

OpenStudy (anonymous):

:D

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