Definition and theorem of derivation, Mathematics

Assignment Help:

Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the point in that interval.

The next theorem illustrates us a very nice relationship among functions which are continuous & those that are differentiable.

Theorem: If  f ( x ) is differentiable at x = a then f ( x ) is continuous at the point x = a.

Note  as well that this theorem does not work in reverse order .  Assume f ( x ) = |x| and take a look at,

1014_derivation7.png

So,f ( x ) = xis continuous at x =0 to sketch the graph of a function.

 

 


Related Discussions:- Definition and theorem of derivation

HELP, a manufacturer is interested in developing a benefit segmentation of ...

a manufacturer is interested in developing a benefit segmentation of the cameramarket.suggest some major benefit segments with market targeting strategies.

#algebra, what is the answer of 6_5x9_4x3(1_2)

what is the answer of 6_5x9_4x3(1_2)

Angles, how to measure missing angle of an adjacent angle

how to measure missing angle of an adjacent angle

Conditional probability: independent events, Conditional Probability: Indep...

Conditional Probability: Independent Events If the probability of an event is subject to a restriction on the sample space, the probability is said to be conditional. Co

Calculate plurality based on the number of voters and candid, Consider an e...

Consider an election with 721 voters. A) If there are 5 candidates, at least x votes are needed to have a plurality of the votes. Find x. B) Suppose that at least 73 votes are n

Markov chain, The Video Club Martin rents movies at "regular price" andat ...

The Video Club Martin rents movies at "regular price" andat "half price". Usually if the films are regularly priced one day, they will be at regular price the next day with probab

Determining and classifying all the critical points, how do you determine ...

how do you determine and classify all the critical points of a function

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