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

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 best

AKASH GOYAL
AskiitiansExpert-IITD

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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