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`        sir how can we find that at what interval the function is increasing or decreasing   what steps should be taken for solving ques. like this`
7 years ago

419 Points
```										Dear Sunil
A function will be increasing if its first derivative is positive and function will be decreasing if first derivative is negative.
To solve such question find out first derivative and check its sign in neighbourhood.
All the bestAKASH GOYALAskiitiansExpert-IITDPlease feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
```
7 years ago
510 Points
```										step -1
find the deriavative of function= df(x)/dx
step-2
put  df(x)/dx=0
let the sol are x=-1 ,4
step-3
now take any number in between  -1 to -infinity ,say 0 then if df(x)/dx at x=o is -ve then function is decreasing  and if value is +ve then function is increasing in this interval.....
eg..
f(x) = x^3-3x+1
d f(x)/dx =3x^2-3
put df(x)/dx=0
x=(-1,1)
at x =-2 ,df(x)/dx=+ve
at x=0  ,df(x)/dx=-ve
at x=2 ,df(x)/dx=+ve
interval in which function increasing is (-infinity,-1)U(1,+infinity)
interval in which function is decreasing is (-1,+1)
approve my ans if u like
```
7 years ago
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