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Original post by Super199
Right I know we use the first derivative to find the gradient. What do we do with the second one? Just a little confused as our teacher didn't really explain why. Thanks
You can use the second derivative to find out if a stationary point on the curve (a point where the first derivative is 0) is a maximum or a minimum
if then the stationary point is a maximum, then the stationary point is a minimumOriginal post by Super199
Right I know we use the first derivative to find the gradient. What do we do with the second one? Just a little confused as our teacher didn't really explain why. Thanks
Sometimes in science, the second derivative is a useful function to know. As a simple example, the second derivative of displacement as a function of time is acceleration.
For mathematical functions, the second derivative can be used to identify turning points (where the graph moves from positive to negative gradient).
Original post by Super199
Right I know we use the first derivative to find the gradient. What do we do with the second one? Just a little confused as our teacher didn't really explain why. Thanks
You use the second derivative to classify stationary points. If it is positive at the point you have a minimum. If it is negative you have a maximum.
Original post by Super199
Right I know we use the first derivative to find the gradient. What do we do with the second one? Just a little confused as our teacher didn't really explain why. Thanks
The derivative always gives rate of change
tells us the rate of change of "something" with respect to x
So gives us the rate of change of the rate of change with respect to x
Original post by Super199
Right I know we use the first derivative to find the gradient. What do we do with the second one? Just a little confused as our teacher didn't really explain why. Thanks
To find the rate of change of the gradient with respect to your independant variable. A nice use of the second derivative is finding whether a stationary point is a minimum, maximum or point of inflection.
Determining the nature of stationary points
Original post by Khallil
A nice use of the second derivative is finding whether a stationary point is a minimum, maximum or point of inflection.
What have you been taught here?
Original post by Khallil
To find the rate of change of the gradient with respect to your independant variable. A nice use of the second derivative is finding whether a stationary point is a minimum, maximum or point of inflection.
What does it mean by point of inflection? I was doing a past paper and it came up, I understand maximum and minimum points but not sure on this? Thanks for the reply as well guys
Is there a third derivative? If so, what does that do?
Original post by Super199
What does it mean by point of inflection? I was doing a past paper and it came up, I understand maximum and minimum points but not sure on this? Thanks for the reply as well guys
You may not need to know about this. Which Awarding Body are you with?
Original post by Mr M
What have you been taught here?
The second derivative being equal to 0 implies that the second derivative test in inconclusive which would mean that the point we're investigating may well be a point of inflection ... right?
Original post by Physics4Life
Is there a third derivative? If so, what does that do?
The first derivative of position is velocity.
The second derivative is acceleration.
The third is jerk (you don't want too big a jerk or your passengers might feel discomfort or bits might fall off your vehicle).
You'll like this next bit.
The fourth derivative is snap, the fifth is crackle and the sixth is pop.
I'm not making this up. It's what physicists call "humour".
Original post by Physics4Life
Is there a third derivative? If so, what does that do?
You can continue to take derivatives as long as you want
Each one gives you the rate of change of the previous one
Original post by Physics4Life
Is there a third derivative? If so, what does that do?
Can use it in kinematics for the rate of change in acceleration, it's called the jerk. We also have something called the jounce which is the fourth derivative of position (so many derivatives!)
Original post by Mr M
You may not need to know about this. Which Awarding Body are you with?
Im with Edexcel for A-level. But I am also doing an AQA further maths GCSE, http://filestore.aqa.org.uk/subjects/AQA-8360-1-QP-JAN13.PDF its question 13c on that. How do I know its a point of inflection?
(edited 10 years ago)
Original post by Khallil
The second derivative being equal to 0 implies that the second derivative test in inconclusive which would mean that the point we're investigating may well be a point of inflection ... right?
Ok. Was just checking you were not saying 0 = inflection. This is a common misconception.
Original post by Super199
Im with Edexcel for A-level. But I am also doing an AQA further GCSE, http://filestore.aqa.org.uk/subjects/AQA-8360-1-QP-JAN13.PDF its question 13c on that. How do I know its a point of inflection?
Test the gradient either side of the stationary point and see whether it is positive or negative.
Original post by Mr M
Test the gradient either side of the stationary point and see whether it is positive or negative.
Oh right. One more question if you don't mind, for question 4 what do those upside down black triangles represent? What topic is that under. May be really stupid it's just I want to read ahead
Original post by Super199
Im with Edexcel for A-level. But I am also doing an AQA further maths GCSE, http://filestore.aqa.org.uk/subjects/AQA-8360-1-QP-JAN13.PDF its question 13c on that. How do I know its a point of inflection?
That's an interesting question because a lot of boards have removed inflexions from A level because people find them confusing!
In this case I think you need to know a bit about cubics - if you draw a typical cubic equation it has 2 turning points, a maximum and a minimum. If you look at the expression for dy/dx that they've given you, it can only be 0 at one point - where x = b. If you think about the shape of possible cubic curves this means you can only have a point of inflexion.
N.B. not sure if this is what the exam board were expecting but it seems the simplest way to explain it
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