Let the function f(x)={sin−1x,−1≤x≤1a−(x−1)2,x>1 has a point of local maxima at x=1, then the minimum value of πa(a>0) is
A
2.00
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B
2.0
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C
2
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Solution
Given : f(x)={sin−1x,−1≤x≤1a−(x−1)2,x>1
Plotting the graph of f(x):
For point of maxima at x=1,f(1−h)<f(1)>f(1+h) as h→0+
From graph it is clear that f(1−h)<f(1) and for f(1)>f(1+h),a should be less than or equal to π2. ⇒a≤π2 ⇒1a≥2π ⇒πa≥2 ∴ minimum value of πa is 2.