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if f(x)=4x^3-x^2-2x+1 and g(x)={min f(t)...

if `f(x)=4x^3-x^2-2x+1` and `g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1}` then `g(1/4)+g(3/4)+g(5/4)` is equal to

A

`7//4`

B

`9//4`

C

`13//4`

D

`5//2`

Text Solution

Verified by Experts

The correct Answer is:
4
`f(X)=12x^(2)-2x-2`
`=2(3x+1)(2x-1)`
`thereforeg(X)={{:(f(x),0lex1//2),(f(1//2),1//2lexle1):}`
`rarr g(1/4)+g(3/4)+g(5/4)`
`=f(1/4)+f(1/2)+g(5/4)`
`=5/2`
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