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

Explain that odd positive integer to be a perfect square, Show that for odd...

Show that for odd positive integer to be a perfect square, it should be of the form 8k +1. Let a=2m+1 Ans: Squaring both sides we get a2 = 4m (m +1) + 1 ∴ product of two

Pythagorean theorem, How do you find the perimeter of an irregular shape us...

How do you find the perimeter of an irregular shape using Pythagorean theorem?

Geometry , Solving for X in isosceles triangles

Solving for X in isosceles triangles

Exponential and geometric model, Exponential and Geometric Model Expo...

Exponential and Geometric Model Exponential model  y = ab x Take log of both sides log y = log a + log b x log y = log a + xlog b Assume log y = Y and log a

Determine the function f ( x ) , Determine the function f ( x ) .       ...

Determine the function f ( x ) .             f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos

Total linear attenuation, Consider the task of identifying a 1 cm thick bre...

Consider the task of identifying a 1 cm thick breast cancer that is embedded inside a 4.2 cm thick fibroglandular breast as depicted in Fig. The cancerous tumor has a cross

Linear programming, how i do project in linear programming in agriculture

how i do project in linear programming in agriculture

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

If all the tickets are the similar price what was the cost, The total ticke...

The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale

How to multiplying rational expressions, how to Multiplying Rational Expres...

how to Multiplying Rational Expressions ? To multiply fractions, or rational expressions, you must multiply the numerators and then multiply the denominators. Here's how it is

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