Question

Ummmm..
Just Curious..
But what does a triple and quadruple differenciation of a function signify graphically??
I know its increasing or decreasing with first derivative, second tells concavity that means how much..
But whats the role of 3rd and 4th???

Answer 1

f''' is acceleration, and f'''' is called a jerk; the speed at which the acceleration is changing

Answer 2

all the derivatives combined tell us how a function is moving at a single point

Answer 3

\(f'''\) is a jerk? I think I am the \(f'''\) you are looking for :-)

Answer 4

spose you wanted to create a polynomial that moved like the sine function

both functions would have to MOVE in the same manner, and all of their derivaties would have to be equal

Answer 5

I don't wanna know it what it means in terms of distance travelled..
Just in general term..

Answer 6

hey @amistre64
I think it's the third derivative that's the jerk?

Answer 7

maybe, i lost count after 1.5

Answer 8

yah its the third derivative..

Answer 9

LOL
Unless f' is the position function and f is... some function whose derivative is the position function XD

Answer 10

Welllllllll...
So can anybody answer my question??
Please??

Answer 11

Well... f'(c) is the slope of the tangent line at the point x = c
f''(c) is the concavity of the graph at the point x = c
f'''(c) is the rate of change of the concavity??? XD

Answer 12

"all the derivatives combined tell us how a function is moving at a single point" by, amistre64

Answer 13

@terenzreignz As much of a guess that was it actually is the right answer!!
:D
:P

Answer 14

yayz :D

Answer 15

concavity is the rate change of the slope, so all that is saying is the rate change of the rate change of the slope, which we can extend to all derivatives.

Answer 16

sin(0) = 0 ; P(x) = 0

sin'(0) = 1 ; P(x) = 0 + x

sin''(0) = 0 ; P(x) = 0 + x +0x^2/2!

sin'''(0) = -1 ; P(x) = 0 + x +0x^2/2! -x^3/3!

sin(x) = P(x)= \(\Large\sum_{n=0}^{\inf}\frac{(-1)^n}{(2n+1)!}x^{2n+1}\)

Answer 17

That just prove sine function is an oscillating function..
nonetheless thank you to all!!
:P

Answer 18

@amistre64 Though if I missed something in your post, Do point out..

Answer 19

i was just demonstrating that the successive derivatives of a function define how it is moving at a single point, and that 2 function that are equal at a single point, and equal at all their successive derivatives are the same at that point.

Since polynomials are so much easier to play with, if we can construct a polynomial to work from, that converges (is the same), at a point or range of points. Then mathing is so much simpler

Answer 20

:D
A very good point Indeed!!

Answer 21

good luck ;)