Interpretation of the second derivative, Mathematics

Assignment Help:

Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative.

If the position of an object is specified by s(t) we know that the velocity is first derivative of the position.

                                                   v (t ) = s′ (t )

First derivative of any velocity is the acceleration of object; however since it is the first derivative of the position function we can also think of the acceleration as the second derivative of the position function.

                                         a (t ) = v′ (t ) = s′′ (t )

Alternate Notation : There is couple of alternate notation for higher order derivatives.  Recall as well that there was a fractional notation for the first derivative.

                                    f ′ ( x ) = df /dx

We should extend this to higher order derivatives.

f ′′ ( x )= d 2 y  / dx                f ′′′ ( x ) = d 3 y/ dx                   etc.


Related Discussions:- Interpretation of the second derivative

Standardizing normal variables, Standardizing Normal Variables Suppose ...

Standardizing Normal Variables Suppose we have a normal population. We can represent it by a normal variable X. Further, we can convert any value of X into a corresponding valu

Power of x, (x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is

(x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is

Simultaneous equations, two rolls of carpet cost £574, the first cost £8 pe...

two rolls of carpet cost £574, the first cost £8 per meter, the second which is 7m longer costs £7 p/m. how many meters are there in each roll

Law of cosines - vector, Theorem a → • b → = ||a → || ||b → || cos• ...

Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha

Word problems involving money, Word Problems Involving Money: The prom...

Word Problems Involving Money: The promoter of a track meet engages a 6,000 seat armory.  He needs to gross $15,000. The price of children's tickets is to be one-half the pric

Give the examples in real world of proportions , Give the Examples in Real ...

Give the Examples in Real World of Proportions? Proportions can be used in cooking. For example, the following is a set of ingredients for a pasta called "Spaghetti All' Amatri

Example of fractional equations, Example of Fractional Equations: Exa...

Example of Fractional Equations: Example: Solve the fractional equation (3x +8)/x +5 =0 Solution: Multiply both sides of the equation by the LCD (x). (x) ((3x

Cartesian graph of density of water - temperature, Cartesian Graph of Densi...

Cartesian Graph of Density of Water - Temperature: Example:  The  density  of  water  was  measured  over  a  range  of  temperatures.   Plot the subsequent recorded data on

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd