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"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-...

`"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4),` then the value of `f'''(1)+f''(2)+f'(3)+f'(4)` equals

A

0

B

50

C

324

D

648

Text Solution

Verified by Experts

The correct Answer is:
648
`f(x)=(x-1)^(4)(x-2)^(3)(x-4)`
`f'''(1)=f''(2)=f'(3)=0`
`f'(x)=(x+1)^(4)(x-2)^(3)(x-3)^(2)cdot1+(x-1)^(4)(x-2)^(3)2(x-3)`
`(x-4)(x+1)^(3)cdot3(x-2)^(2)+(x-3)^(2)+(x-4)+4(x-1)^(3)(x-2)^(3)(x-3)^(2)(x-4)`
`f'(4)=3^(4)xx2^(3)xx1=3xx6^(3)`
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