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Find the points of minima for f(x)=int0^...

Find the points of minima for `f(x)=int_0^x t(t-1)(t-2)dt`

Text Solution

Verified by Experts

The correct Answer is:
`x=0,2`
`f(x)=int_(0)^(x)t(t-1)(t-2)dt`
Let `f'(x)=x(x-1)(x-2)=0`
`:. X=0,1` or 2
At `x=0` and `2,f'(x)` changes sign form -ve to +ve.
Hence `x=0` and 2 are points of minima.
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