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Increasing and Decreasing Functions at a Point Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Increasing and Decreasing Functions at a Point Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is the definition of an increasing function at a point? |  |
Ans. An increasing function at a point is a function in which the values of the function are greater as the input values increase. In other words, if the function f(x) is increasing at a point a, it means that for any two values, a and b, where a < b, the value of f(a) is less than or equal to f(b).
| 2. How can we determine if a function is increasing or decreasing at a specific point? | |
Ans. To determine if a function is increasing or decreasing at a specific point, we can analyze the behavior of the function's derivative at that point. If the derivative is positive, the function is increasing at that point. If the derivative is negative, the function is decreasing at that point.
| 3. What does it mean for a function to be decreasing at a point? | |
Ans. A function is said to be decreasing at a point if the values of the function decrease as the input values increase. In other words, if the function f(x) is decreasing at a point a, it means that for any two values, a and b, where a < b, the value of f(a) is greater than or equal to f(b).
| 4. Can a function be both increasing and decreasing at the same point? | |
Ans. No, a function cannot be both increasing and decreasing at the same point. A function can be either increasing or decreasing at a specific point, but not both simultaneously. This is because the definition of an increasing function contradicts the definition of a decreasing function.
| 5. How can we determine if a function has a maximum or minimum at a specific point? | |
Ans. To determine if a function has a maximum or minimum at a specific point, we can analyze the behavior of the function's derivative around that point. If the derivative changes sign from positive to negative, the function has a maximum at that point. If the derivative changes sign from negative to positive, the function has a minimum at that point.
Text Transcript from Video
in this video let's talk about
increasing decreasing functions the name
is written over here increasing
decreasing functions we already know
some applications in the chapter of
applications of derivatives like
application of derivatives are in
various areas like finding maxima minima
derivative as a rate measure and so on
one of the applications is the study of
increasing decreasing functions suppose
for this particular topic let's consider
Y is equal to X square y is equal to X
square means a parabola a parabola which
is the upward parabola now I already
know that different values of x will
give me different values of Y suppose my
x-value and y-value i need to plot my x
value if I put is 0 then what is Y X
square which is 0 if my x value is 1 y
square Y is X square which is again 1
what if my x value is minus 1 minus 1
square is also 1 so that means different
values of X are giving me some values of
Y when I have to plot it I definitely
get an upward parabola by far definitely
we are not going to use all the values
but a rough approximation will give me a
parabola like this now I have 0 over
here that is for sure and different
different values over there it must be
noted that if one is here the F 1 the F
1 should be equal to F of minus 1 as you
see that one is also giving me 1 minus 1
is also giving me 1 similarly in case of
minus 2 n 2 and so on so basically
increasing decreasing functions what is
it all about it says that suppose I take
the first quadrant this is the first
quadrant you definitely know it in the
first quadrant you see that when you
increase the values of X because here it
is 1 definitely later it will be 2 then
3 and so on on increasing the values of
X you also get an increase in violence
see the height was earlier
as much then it will crease they did
increased and so on so increasing values
of X giving me increase in values of Y
that to me is in the first quadrant y is
equal to X square grout behaves as an
increasing function right but what about
decreasing one let's move to this
quadrant which is quadrant number two
now in quadrant number two definitely
again will be having some values minus 1
minus 2 minus 3 and so on and I know
that as soon as I increase the values of
X say minus 3 to minus a minus 2 is
increasing here it is increasing in the
values of X I see that my high first was
this much then it decrease then decrease
in decrease so increasing values of X
giving me a decrease in values of Y that
means it is a decreasing function see
the height was this much then it
decreased decreased decrease so it's
like decreasing function here it's like
increasing function so in this example
in one particular graph only we have
understood what is increasing and
decreasing function this is a very very
brief idea to it in the next videos
we'll be seeing more detail on this
topic
increasing decreasing functions the name
is written over here increasing
decreasing functions we already know
some applications in the chapter of
applications of derivatives like
application of derivatives are in
various areas like finding maxima minima
derivative as a rate measure and so on
one of the applications is the study of
increasing decreasing functions suppose
for this particular topic let's consider
Y is equal to X square y is equal to X
square means a parabola a parabola which
is the upward parabola now I already
know that different values of x will
give me different values of Y suppose my
x-value and y-value i need to plot my x
value if I put is 0 then what is Y X
square which is 0 if my x value is 1 y
square Y is X square which is again 1
what if my x value is minus 1 minus 1
square is also 1 so that means different
values of X are giving me some values of
Y when I have to plot it I definitely
get an upward parabola by far definitely
we are not going to use all the values
but a rough approximation will give me a
parabola like this now I have 0 over
here that is for sure and different
different values over there it must be
noted that if one is here the F 1 the F
1 should be equal to F of minus 1 as you
see that one is also giving me 1 minus 1
is also giving me 1 similarly in case of
minus 2 n 2 and so on so basically
increasing decreasing functions what is
it all about it says that suppose I take
the first quadrant this is the first
quadrant you definitely know it in the
first quadrant you see that when you
increase the values of X because here it
is 1 definitely later it will be 2 then
3 and so on on increasing the values of
X you also get an increase in violence
see the height was earlier
as much then it will crease they did
increased and so on so increasing values
of X giving me increase in values of Y
that to me is in the first quadrant y is
equal to X square grout behaves as an
increasing function right but what about
decreasing one let's move to this
quadrant which is quadrant number two
now in quadrant number two definitely
again will be having some values minus 1
minus 2 minus 3 and so on and I know
that as soon as I increase the values of
X say minus 3 to minus a minus 2 is
increasing here it is increasing in the
values of X I see that my high first was
this much then it decrease then decrease
in decrease so increasing values of X
giving me a decrease in values of Y that
means it is a decreasing function see
the height was this much then it
decreased decreased decrease so it's
like decreasing function here it's like
increasing function so in this example
in one particular graph only we have
understood what is increasing and
decreasing function this is a very very
brief idea to it in the next videos
we'll be seeing more detail on this
topic
About this Video
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Dec 23, 2024 Last updated |
Video Description: Increasing and Decreasing Functions at a Point for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
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