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anonymous
 5 years ago
WHY do we use the second derivative to find the inflection point? Couldn't quite grasp the concept.
anonymous
 5 years ago
WHY do we use the second derivative to find the inflection point? Couldn't quite grasp the concept.

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shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0The first derivative will tell you where the slope of the function is 0. This is a prerequisite for an inflection point.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0The other requirement is that the function change `directions' from one side of the point to the other.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0In order for that to happen, the slope must go from being negative to being positive or positive to negative. The second derivative can tell us whether or not that is happening.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, that's completely wrong.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Started explaining the wrong concept.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Let's start from scratch! An inflection point is where a function changes from being concave upwards to being concave downwards.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Functions that are concave upwards have a slope that is increasing (either becoming more positive or less negative), and those that are concave downwards have a slope that is decreasing (either becoming less positive or more negative).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Remember the inflection point tells us where the concavity of the underlying function changes from concave up to concave down.. So tracing this through the first derivative....an inflection point (on the original function) becomes a max or min on the first derivative function and therefore a zero on the second derivative function. That is why it is easiest to identify the inflection points from the second derivative....they are the zeros!

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0To convince yourself of this, you can do a quick sketch of a regular parabola, which is concave up, and sketch tangent lines at the edges and in the middle of the curvatures. You should be able to see that the tangent lines go from a very negative slope to a midnegative slope to a zero slope to a midpositive slope to a very positive slope. You can do the same with a parabola flipped over the y axis to convince yourself of how concave down implies a tangent slope that is decreasing. Then yes, apply descartes's information :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you both! But I guess I am confused with what the second derivative IS.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know that the first derivative is the expression for the slope of the tangent line; therefore, when it is zero, and there is a change in sign, we can find the extrema. But why is it when the second derivative=0, we find the inflection point? descartes sort of lost me on tracing through the first derivative...

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So, the first derivative describes the slope of the function at any given point.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Basically it's a visualization (or description) of how the slope changes.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Similarly, the second derivative describes the slope of the *first* derivative at any given point.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i depende on how the slope is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks. I am still sort of muddy. Descartes said, "an inflection point (on the original function) becomes a max or min on the first derivative function and therefore a zero on the second derivative function. "

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0In terms of the first function, it describes how fast and in what direction the function's slope is changing.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So, as I was saying earlier, the inflection point is when the function changes from concave up to down or vice versa.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0This means that the *slope* of the function changes from *increasing* to *decreasing* or the other way around.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0This means that the slope of the first *derivative* changes from *positive* to *negative* or vice versa.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Which means that the *value* of the *second* derivative changes from positive to negative or vice versa.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0And between positive and negative is zero :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that can make a diffrence in the question itself so the slop might be *increseing* or *decreseung* ethir way

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make a little more sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0'slope* of the function changes from *increasing* to *decreasing* or the other way around"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you mean the original function?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isn't that the extrema though?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait. I think I get it...

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0I mean the original function, yes. And the extrema are where the slope of the original function changes from positive to negative, not where it changes from actually increasing to decreasing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:( what is the difference? I'm sorry.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Increasing is a description of the *rate* at which something is changing. So if the slope of the original function is increasing, its slope is getting more positive *faster*. Instead of just getting more positive.
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