What go the third derivative signify?

The derivative the A through respect to B tells you the price at which A changes when B changes.

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The second derivative is the derivative of the derivative: the rate of adjust of the rate of change.

The third derivative is the derivative that the derivative that the derivative: the rate of adjust of the rate of adjust of the price of change.

The more significance of this counts on what A and also B are.

If you are thinking of A together the elevation of a curve, v B as the x-axis, then the very first derivative is the slope of the curve (rate of readjust of the elevation of the curve). The 2nd derivative is the rate of change of the slope, or the curvature. If the curve is curving upwards, prefer a smile, yes sir a positive second derivative; if it’s curving downwards prefer a frown, there"s a an adverse second derivative; whereby the curve is a right line, the 2nd derivative is zero.

In that case the third derivative is the price of change of the curviness. Ns don’t know an additional name for it, yet if the curve goes from gift concave downwards to gift concave upwards, you have the right to conclude the 3rd derivative is positive.

On the various other hand, if A is position and also B is time, then the derivative the A v respect come B is velocity. The second derivative is the rate of change of velocity, or acceleration. The third derivative, the rate of adjust of acceleration, is called jerk.

When your vehicle is not accelerating, you’re not being pushed earlier in her seat in ~ all. Once your automobile is increasing mightily, you"re pushed against the back of her seat. The faster the shift between these two states, the greater the jerk.

In my experience, at the very least 99% that all supplies of the word “jerk” (with this meaning) happen in sentence of the form, “Hey, go you understand that the third time derivative of place is dubbed jerk?” The continuing to be one percent of the time, the word is offered seriously by automobile safety engineers and the like.

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The 4th and higher time derivatives of place are not offered often sufficient for there to it is in a serious developed word because that them. Snap has actually been proposed for the 4th derivative, naturally followed by crackle and pop because that the fifth and sixth derivatives.