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# The value of 'a' for which the functionƒ(x)={ -x3 + sin-1 a ,when 0

Jitender Singh IIT Delhi
6 years ago
Ans:
$f(x) = {-x^{3}+sin^{-1}a, 0< x<1}$
$= {x, x\geq 1}$
The value of f(x) at x = 1 is1.For the function to have minimum at 1, left hand neighbourhood of x = 1 should be greater than f(1).
$-(1)^{3}+sin^{-1}a> f(1)> 1$
$sin^{-1}a> 2$
which is not possible because
$-1\leq sin^{-1}a\leq 1$
So there is no value of ‘a’ for which f(x) has minimum at 1.
Thanks & Regards
Jitender Singh
IIT Delhi
Jitender Singh
13 Points
6 years ago
Ans:
There is a small mistake in the above answer.
-pi/2 =-1a =

Thanks & Regards
Jitender Singh
IIT Delhi