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Gemiddelde gradiënt van ander funksies

Ons kan die konsep van die gemiddelde gradiënt uitbrei na enige funksie. Die gemiddelde gradiënt van enige nie-reglynige funksie hang af van die gekose interval want dit is die gradiënt van die reguitlyn wat deur die twee gekose punte gaan; dit is nie konstant nie. Ons kan dus die formule gebruik wat ons gebruik het vir die gemiddelde gradiënt van paraboliese funksies en dit toepas op enige ander funksie. Ons sal die gemiddelde gradiënt van twee funksies hier ondersoek: die eksponensiële funksie en die hiperboliese funksie.

Gemiddelde gradiënt van eksponensiële funksies

Veronderstel ons word gevra om die gemiddelde gradiënt van die funksie g(x) = 3 . 2 x + 2 tussen die punte ( - 4 ; 2,2 ) en ( - 0,6 ; 4 ) te vind. Dit word getoon in [link] .

Die gemiddelde gradiënt vir 'n eksponensiële funksie
As ons die formule gebruik, vind ons:
y 2 - y 1 x 2 - x 1 = 4 - 2,2 ( - 0,6 ) - ( - 4 ) = 1,8 - 0,6 + 4 = 1,8 5,2 = 0,35

Gemiddelde gradiënt van hiperboliese funksies

Gestel ons word byvoorbeeld gevra om die gemiddelde gradiënte te vind van die funksie g ( x ) = 2 x + 2 tussen die punte ( - 4 ; - 2,5 ) en ( 0,5 ; 6 ) ; asook tussen ( - 4 ; 2,2 ) en ( - 0,6 ; 4 ) . Dit word getoon in [link] .

Die gemiddelde gradiënt vir 'n hiperboliese funksie

Vir die eerste punt kry ons:

y 2 - y 1 x 2 - x 1 = ( - 2,5 ) - 1 ( - 4 ) - 0,5 = - 3,5 - 4,5 = 0,78
Soortgelyk, die gemiddelde gradiënt tussen die tweede stel punte sal wees 0,53 .

Opsomming

  • Die gemiddelde gradiënt tussen twee punte is: y 2 - y 1 x 2 - x 1
  • Die gemiddelde gradiënt van 'n reguitlynfunksie is dieselfde oor enige interval (tussen enige twee punte) op die reguitlyn.
  • Die gemiddelde gradiënt van 'n paraboliese funksie hang af van die punte (interval) wat gekies is; dit is die gradiënt van die reguitlyn wat deur die gekose punte gaan.
  • Ons kan die konsep van gemiddelde gradiënt uitbrei na enige funksie.

Einde van die hoofstuk oefeninge

  1. 'n Voorwerp beweeg volgens die funksie d = 2 t 2 + 1 , waar d die afstand in meter is en t die tyd in sekondes. Bereken die gemiddelde snelheid van die voorwerp tussen die tweede en derde sekondes. Die snelheid is die gradiënt van die funksie d
  2. Gegee: f ( x ) = x 3 - 6 x . Bepaal die gemiddelde gradiënt tussen die punte x = 1 en x = 4 .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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