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Question

The value of λ for which the function f(x)=λx32λx2+(λ+1)x+3λ is increasing through out number line.

A
λ(3,3)
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B
λ(3,0)
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C
λ(0,3)
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D
λ(1,3)
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Solution

The correct option is A λ(0,3)
Given,
f(x)= λx32λx2+(λ+1)x+3λ
for increasing f(x)>0
and f(x)=3λx24λx+(λ+1)
3λx24λx+(λ+1)>0
for this D<0
(4λ)24(3λ)(λ+1)<0
16λ2(12λ2+12λ)<0
16λ212λ212λ<0
4λ212λ<0
λ23λ<0
λ(λ3)<0
Hence, λ ϵ(0,3)

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