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Question

The number of integral value(s) of a for which f(x)=a23+sinx, 0<x<π21+cosx, π2x<π has a point of local maxima at x=π2, is

A
3.0
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B
3
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C
3.00
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Solution

Given : f(x)=a23+sinx, 0<x<π21+cosx, π2x<π, has a point of local maxima at x=π2
f(π2)<f(π2)>f(π2+)
a23+1<1+0 and cosx is decreasing in [π2,π], so f(π2)>f(π2+)
a23<0
a(3,3)
So, possible integral values of a is 1,0,1

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