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The value of 'a' for which the function

ƒ(x)={ -x³+ sin^-1a ,when 0

Tapasranjan Das , 15 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 11 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

Last Activity: 11 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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