Interpretations of derivatives, Mathematics

Assignment Help:

Interpretations of derivatives.

Example:   Find out the equation of the tangent line to

                                      x2 + y 2  =9

at the point (2, √5 ) .

Solution

We have to be given both the x & the y values of the point.  Notice that this point does lie on the graph of the circle (you can verify by plugging the points into the equation) and thus it's okay to talk regarding the tangent line at this point.

Recall that to write the tangent line we required is the slope of the tangent line and it is nothing more than the derivative evaluated at the specified point. 

Then the tangent line is.

                                      y =     √5 - 2/ √5  ( x - 2)

Now, let's work on some more examples. 

There is a simple way to remember how to do the chain rule in these problems.  Really the chain rule tells us to differentiate the function as usually we would, except we have to add on a derivative of the inside function.  In implicit differentiation it means that every time we are differentiating a term along y in it the inside function is the y and we will have to add a  y′ onto the term as that will be the derivative of the inside function. Let's see a couple of examples.


Related Discussions:- Interpretations of derivatives

Tied rankings, Tied Rankings A slight adjustment to the formula is mad...

Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied

Series solutions to differential equation, Before we find into finding seri...

Before we find into finding series solutions to differential equations we require determining when we can get series solutions to differential equations. Therefore, let's start wit

RATIO, 3 years to 104 weeks,express answer in ratio

3 years to 104 weeks,express answer in ratio

Solving equations, darien agrees to sponsor her sister $8 plus $1 for every...

darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money

How to find x?, How can I solve x in a circle? For example.. m

How can I solve x in a circle? For example.. m

Calculate the area of circle, Calculate the area of CIRCLE ? A circle i...

Calculate the area of CIRCLE ? A circle is a set of all points that are at a given distance from a center point. The diameter (d) of a circle is the length of a line that goes

Calculate annual interest rate, 1. What is the present value of a security ...

1. What is the present value of a security that will pay $15,000 in 15 years if securities of equal risk pay 8.9% annually? Round your answer to the nearest cent. 475,858.20

Given a differential equation will a solution exist?, All differential equa...

All differential equations will doesn't have solutions thus it's useful to identify ahead of time if there is a solution or not. Why waste our time trying to get something that doe

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