What's the meaning of 3rd derivative?

Question

1rst is to know if a function is increasing/decreasing.

2nd is know if there is a minimum/maximum (peek).

Answer 1

3rd derivative are points of inflection.

Answer 2

The first derivative gives the change of the original function. If the function has a peak or a "valley" (max/min) then the derivative is zero. The second derivative is used to determine if the zero you see in the first derivative is a max (peak) or min (valley). The second derivative indicates if the function is concave up, concave down, or has a point of inflection.

If the second derivative is positive at the same x value that the first derivative is zero, then you have a min (valley).

If the second derivative is negative at the same x value the first derivative is zero, then you have a max (peak).

If the second derivative is zero at the same x value the first derivative is zero, then you have a point of inflection. The most common example is where x = 0 for the function y = x^3.

For sketching graphs, the third derivative is not used.

Answer 3

The only real meaning is that the 3rd derivative is the derivative after the 2nd derivative. In the physical world if your function described distance with respect to time. The 1st derivative would be velocity, the 2nd would be acceleration and the 3rd would be change in acceleration.

Answer 4

We can understand the physical meaning in this way. If we take the derivative of Displacement we get Velocity. This when further differentiated gives you Acceleration. This when differentiated again[Third Derivative] gives you Jerk, which is the rate of change of acceleration. This is an important parameter which is material while designing Rocket Motors for space applications as also in Ejection Seats which are escape aids for pilot in a fighter aircraft to escape during an emergency.

Answer 5

3rd Derivative

Answer 6

first off your definitions arre incorrect:

First derivative (y') is shows intervals on which the function is increasing/decreasing, but zeros and values at which y' is undefined are called critical points and are where you look for min and max values. and also if y is position, y' is velocity.

the second derivative (y'') shows concavity and its critical points are possible points of inflection for y and possible max or min for y'. y'' is acceleration

the third derivative (y''') is not widely used, but it can be useful in evaluation of y' and y'' (it is the second deriv of y' and the first deriv of y''). it is also known as jerk which is basically change in acceleration.

Answer 7

This Site Might Help You.

RE:
What's the meaning of 3rd derivative?
1rst is to know if a function is increasing/decreasing.

2nd is know if there is a minimum/maximum (peek).

Answer 8

yes and no integrating is taking the antiderivative, but when you are looking at an integral of a function not defined for [a,b], then it is the general form and make sure you add +c to the end of it. the derivative of 2x^3 +1-2=6x^2 when you integrate you undo that, but might not know the constant was 1 or 2 or -1, so you just name it "c"

Answer 9

the third derivative is a mathematical construct. ONE way of using this construct is to use it to describe the rate of change of the acceleration of a moving body. this might mean that the magnitude of the acceleration is changing or it might mean that the direction of the acceleration is changing. keep in mind that this is only ONE way of applying this area of mathematics.

Answer 10

Wow! thank you! Exactly what I was searching for. I looked for the answers on other websites but I couldn't find them.

Answer 11

the rate of change of acceleration, is technically known as jerk (symbol j). Jerk is a vector but may also be used loosely as a scalar quantity because there is not a separate term for the magnitude