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The value of 'a' for which the function ƒ(x)={ -x 3 + sin -1 a ,when 0

The value of 'a' for which the function


ƒ(x)={ -x3 + sin-1 a ,when 0

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
askIITians Faculty
Jitender Singh
13 Points
9 years ago
Ans:
There is a small mistake in the above answer.
-pi/2 =-1a =
 
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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