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Question

Let the function f(x)={sin1x,1x1a(x1)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)={sin1x, 1x1a(x1)2, x>1
Plotting the graph of f(x):

For point of maxima at x=1,f(1h)<f(1)>f(1+h) as h0+
From graph it is clear that f(1h)<f(1) and for f(1)>f(1+h), a should be less than or equal to π2.
aπ2
1a2π
πa2
minimum value of πa is 2.

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