The value of a for which the function f(x)=(4a−3)(x+log5)+2(a−7)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)=(4a−3)(x+log5)+2(a−7)cot(x/2)sin2x/2f(x)=(4a−3)(x+log5)+(a−7)(2×cot(x/2)sin2x/2)f(x)=(4a−3)(x+log5)+(a−7)(sinx)f′(x)=(4a−3)+(a−7)(cosx)