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

Multiplying fractions involving negative numbers, Q. Multiplying Fractions ...

Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe

Straight Line, can i known the all equations under this lesson with explana...

can i known the all equations under this lesson with explanations n examples. please..

Sketch the graph of the derivative of this function f '( x), Below is the s...

Below is the sketch of a function f ( x ) . Sketch the graph of the derivative of this function f ′ ( x ) . Solution : At first glance it seems to an all however impossib

How many permutations of the letters a b c d e f g h, How many permutations...

How many permutations of the letters A B C D E F G H consist of string DEF?    Ans: It is the dilemma of finding number of words that can be formed along with the given 8 lette

Definition of a function, Definition of a Function Now we need to move...

Definition of a Function Now we need to move into the second topic of this chapter.  Before we do that however we must look a quick definition taken care of.

Binary to decimal, 01010011 01100101 01101101 01110000 01100101 01110010 00...

01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001

Surds and logarithms, what are these all about and could i have some exampl...

what are these all about and could i have some examples of them please

form a pythagorean triple, A Pythagorean triple is a set of positive integ...

A Pythagorean triple is a set of positive integers (a,b,c) like  a2 + b2 = c2.  Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r

What are the angles of depression from observing position, In Figure, what ...

In Figure, what are the angles of depression from the observing positions O 1 and O 2 of the object at A?

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