The function f ( x ) = ∫ 1 x { 2 ( t − 1 ) ( t − 2 ) 3 + 3 ( t − 1 ) 2 ( t − 2 ) 2 } dt attains its maximum at x is equal to

Question

The function f ( x ) = ∫ 1 x ​ { 2 ( t − 1 ) ( t − 2 ) 3 + 3 ( t − 1 ) 2 ( t − 2 ) 2 } dt attains its maximum at x is equal to

TestHub · Accepted Answer

f ′ ( x ) = 2 ( x − 1 ) ( x − 2 ) 3 + 3 ( x − 1 ) 2 ( x − 2 ) 2 ​ = ( x − 1 ) ( x − 2 ) 2 { 2 ( x − 2 ) + 3 ( x − 1 )} ​ = ( x − 1 ) ( x − 2 ) 2 ( 5 x − 7 ) ​ sign change of f ′ ( x ) from +ve to -ve at x = 1 ∴ maximum at x = 1 .

Mathematics - Definite Integration Question with Solution | TestHub

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