Application of derivatives Ex-6.2|Increasing|
#derivatives #class12maths #increasinganddecreasingfunctions #increasingfunctions
In this video we will discuss concept of increasing/decreasing function with the help of graphs of function or using definition.
A continuous function in an interval (a, b) is :
(i) strictly increasing if for all x1, x2 ∈ (a, b), x1less than x2 ⇒ f (x1) less than f (x2) or for all
x ∈ (a, b), f ′ (x) greater than 0
(ii) strictly decreasing if for all x1, x2 ∈ (a, b), x1 Less than x2 ⇒ f (x1) greater than f (x2) or for all x ∈ (a, b), f ′(x) less than 0
6.1.5 Theorem : Let f be a continuous function on [a, b] and differentiable in (a, b) then
(i) f is increasing in [a, b] if f ′ (x) greater than 0 for each x ∈ (a, b)
(ii) f is decreasing in [a, b] if f ′ (x) Less than 0 for each x ∈ (a, b)
(iii) f is a constant function in [a, b] if f ′ (x) = 0 for each x ∈ (a,b)
#derivatives #differentiation #rajsthanboard #hpbose #cbseboard #class12maths #biharboard #nda #ndapreparation #nda2023 #ndaexam #ndamaths #mpboard #mpboardclass12 #jeemains #jee #jeemaths #jee2024 #jeemain #applicationofderivativesclass12 #applicationofdifferentiation #applicationsofderivatives
Upcoming courses for :
#NDA - 2023(I) for 12th studying or passed students.(Online mode)
#NDA-2024(I) & (II) for 12th studying or 11th studying students(Online mode)
#JEE(Mains/Adv)-2024 for 12th studying or passed students(Online mode)
#JEE(Mains/Adv)-2025 for 11th studying students(Online mode)
#Foundation courses for (8th, 9th, 10th)
#foundation #foundationcourse #derivatives #biharboard #class12maths #differentiation #ndapreparation #nda2023 #nda #ndaexam #nda #jee2024 #jee2025
WhatsApp for details : 9872156055
[email protected]