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Question

The values of p for which the function f(x)=(p+41p1)x53x+ln5 decreases for all real x is

A
(,)
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B
[4,3212](1,)
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C
[3,5272](2,)
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D
[1,)
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Solution

The correct option is B [4,3212](1,)
Given f(x)=(p+41p1)x53x+ln5
f(x)=(p+41p1)5x43
Since, f(x) is decreasing,
f(x)<0
(p+41p1)5x43<0xϵR
p+41p10
If 4p<1 then
p+41p
p+412p+p2
p23p30
p3212or3+212p
pϵ[4,3212]
If p>1 then p+41p
Always true for p>1
pϵ[4,3212](1,)

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