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Question

The value of a for which the function f(x)=(4a3)(x+log5)+2(a7)cotx2sin2x2 does not possess critical points is

A
(,43)
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B
(,1)
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C
[1,)
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D
(2,)
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Solution

The correct options are
A (,43)
C (2,)
f(x)=(4a3)(x+log5)+2(a7)cot(x/2)sin2x/2f(x)=(4a3)(x+log5)+(a7)(2×cot(x/2)sin2x/2)f(x)=(4a3)(x+log5)+(a7)(sin x)f(x)=(4a3)+(a7)(cos x)
f(x) will not be zero
if (4a3)>(a7)
2a>4
a>2
or
4a3<(a7)
5a<10
a<2

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