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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???

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f''' is acceleration, and f'''' is called a jerk; the speed at which the acceleration is changing
all the derivatives combined tell us how a function is moving at a single point
\(f'''\) is a jerk? I think I am the \(f'''\) you are looking for :-)

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Other answers:

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
I don't wanna know it what it means in terms of distance travelled.. Just in general term..
hey @amistre64 I think it's the third derivative that's the jerk?
maybe, i lost count after 1.5
yah its the third derivative..
LOL Unless f' is the position function and f is... some function whose derivative is the position function XD
Welllllllll... So can anybody answer my question?? Please??
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
"all the derivatives combined tell us how a function is moving at a single point" by, amistre64
@terenzreignz As much of a guess that was it actually is the right answer!! :D :P
yayz :D
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.
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)= \(\Large\sum_{n=0}^{\inf}\frac{(-1)^n}{(2n+1)!}x^{2n+1}\)
That just prove sine function is an oscillating function.. nonetheless thank you to all!! :P
@amistre64 Though if I missed something in your post, Do point out..
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
:D A very good point Indeed!!
good luck ;)

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