00:01
As students, we are given a function, we just need to solve those a -b -z part.
00:03
So we will start with a part.
00:05
What we are given, function f -x is equal to x to the power 4 times e to the power minus x, okay? first of all, we just need to find the intervals in which f is increasing and decreasing.
00:14
So in order to find those, we just need to find f -b -x, okay? so when we take x to the power 4 as, when we consider treat x to the power 4 as a constant, the derivation of e to the power minus x will be minus of e to the power minus x okay plus when we treat e to the power minus x constant the derivation of x to the power 4 will be 4 x cube okay so now what we can understand f x can be written as when we take minus of sorry e to the power minus x times here what what things can we take common x cube okay my e to the power minus x times x cube what we will get here it will be minus x okay students plus here it will be 4 okay now what we can do here in order to find it for increasing for increasing we just need to make f dash x f dash x is greater than 0 okay now so basically what we can do e to the power minus x times x cube times 4 minus x is greater than 0 okay it is always positive so we can make it in a 0 so x cube times 4 minus x x x x x times 4 minus x is always greater than 0.
01:28
Okay, students, so we can just write it as x cube times of x minus 4 is less than 0.
01:34
It means x times of x minus 4 can be written as less than 0.
01:39
Okay.
01:40
Now we will go for the vivekar method.
01:43
It is 4.
01:44
It is 0 plus minus plus.
01:46
Okay.
01:47
We are supposed to know that we just need to go for the less than values.
01:50
So x belongs to 0 .4.
01:53
Okay, students...