Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = (x2 − 1)3, [−1, 2]

Given :

To Find :

the absolute minimum and absolute maximum values of f on the given interval

[-1,2] .

Solution :

Now , getting first order differential equation and equating its equal to zero.

So , x=0 is critical point .

Now , coefficient of is positive .

Therefore , it is increasing function after  x=0 .

So , min value will be at , x=0.

And maximum value will be the maximum at the x=2 because it is increasing function .

Therefore , max and min value is 9 and -3 respectively .

Hence , this is the required solution .

step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)