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Question

Let f(x)=x4axx2,(a>0). Then f(x) has range in-

A
(0,3a)
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B
(a,4a)
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C
(0,4a)
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D
None of the above
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Solution

The correct option is C (0,4a)
f(x)=x4axx2
Differentiate w.r.t x
f1(x)=xα4axx2×(4a2x)+4axx2
=x(4a2x)α4axx2+4axx2
=xα(2xa)α4axx2+4axx2
=(2xa)x4axx2+4axx2
Equatef1(x)=0
0=(2xa)x4axx2+4axx2
4axx2=(2xa)x4axx2
(4axx2)2=(2xa)x
4axx2=2axx2
2ax=0
x=0
So factor is xx(4ax)=0
x=0orx(4ax)=0
4axx2=0
x2=4ax
x=4a
SInce the function has the range (0,4a)
(0,4a) falls in this range

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