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

Experiments probabillity of compound events, what is the expiremental proba...

what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62

The multiplication algorithm, THE MULTIPLICATION ALGORITHM :  Some Class 3...

THE MULTIPLICATION ALGORITHM :  Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests bas

Math, a business is owned by three people.the first owns 1/12 of the busine...

a business is owned by three people.the first owns 1/12 of the business and the second owns 1/6 of the business. what fractional part of the business is owned by the third person

Integration, find the area bounded by the curve y=5x^2-4x+3 from the limit ...

find the area bounded by the curve y=5x^2-4x+3 from the limit x=0 to x=5

Index of summation - sequences and series, Index of summation - Sequences a...

Index of summation - Sequences and Series Here now, in the i is termed as the index of summation or just index for short and note that the letter we employ to represent

What is a function, What is a Function, Anyway? Domain? Range? Next tim...

What is a Function, Anyway? Domain? Range? Next time you're at a fast-food restaurant, take a look at the price list. It may look something like this: • Hamburger.............

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

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