The number of integral value(s) of a for which f(x)=⎧⎪⎨⎪⎩a2−3+sinx,0<x<π21+cosx,π2≤x<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)=⎧⎪⎨⎪⎩a2−3+sinx,0<x<π21+cosx,π2≤x<π, has a point of local maxima at x=π2 ⇒f(π2−)<f(π2)>f(π2+) ⇒a2−3+1<1+0 and cosx is decreasing in [π2,π], so f(π2)>f(π2+) ⇒a2−3<0 ⇒a∈(−√3,√3)
So, possible integral values of a is −1,0,1