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CBSE Class 12-science Answered

What will be the answer for this question?
Asked by dineshchem108 | 09 Oct, 2019, 07:04: PM
Expert Answer
Let f(x)=x4e-x2
f apostrophe left parenthesis x right parenthesis equals e to the power of negative x squared end exponent 4 x cubed plus x to the power of 4 e to the power of negative x squared end exponent left parenthesis negative 2 x right parenthesis equals 2 x cubed e to the power of negative x squared end exponent open parentheses 2 minus x squared close parentheses T a k e space f apostrophe left parenthesis x right parenthesis equals 0 rightwards double arrow 2 x cubed e to the power of negative x squared end exponent open parentheses 2 minus x squared close parentheses equals 0 rightwards double arrow x cubed equals 0 space o r space 2 minus x squared equals 0 rightwards double arrow x equals 0 space o r space x squared equals 2 rightwards double arrow x equals 0 space o r space x equals plus-or-minus square root of 2 f " left parenthesis x right parenthesis equals 12 x squared e to the power of negative x squared end exponent plus 4 x cubed e to the power of negative x squared end exponent left parenthesis negative 2 x right parenthesis minus 10 x to the power of 4 e to the power of negative x squared end exponent minus 2 x to the power of 5 e to the power of negative x squared end exponent left parenthesis negative 2 x right parenthesis rightwards double arrow f " left parenthesis x right parenthesis equals e to the power of negative x squared end exponent open parentheses 12 x squared minus 18 x to the power of 4 plus 4 x to the power of 6 close parentheses f " left parenthesis 0 right parenthesis equals 0 comma space f " left parenthesis square root of 2 right parenthesis equals e to the power of negative 2 end exponent open parentheses 12 cross times 2 minus 18 cross times 4 plus 4 cross times 8 close parentheses equals e to the power of negative 2 end exponent open parentheses 24 minus 72 plus 32 close parentheses equals negative 16 e to the power of negative 2 end exponent less than 0 S o comma space square root of 2 space i s space t h e space m a x i m a T h u s comma space t h e space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis space i s space f left parenthesis square root of 2 right parenthesis equals open parentheses square root of 2 close parentheses to the power of 4 e to the power of negative open parentheses square root of 2 close parentheses squared end exponent equals 4 e to the power of negative 2 end exponent H e n c e comma space o p t i o n space D space i s space c o r r e c t.
Answered by Renu Varma | 10 Oct, 2019, 11:44: AM

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