Let f (x ) be a polynomial of degree 6 in x, in which the coefficient of x^6is unity and it has extrema at x=-1 and x=1 . If limx 0 0.05em f (x )x^3=1, then 5.f (2 ) is equal to

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Correct answer: 144. (144) f (x )=x^6+ax^5+bx^4+x^3 ∴f^ ' (x )=6x^5+5ax^4+4bx^3+3x^2 Roots 1-1 ∴6+5a+4b+3=0 \&-6+5a-4b+3=0 solving a=- 35b=- 32 ∴f (x )=x^6-x^5- 32x^4+x^3 ∴5.f (2 )=5(64- 965-24+8)=144

$Let f (x) be a polynomial of degree 6 in x, in which the coefficient of x^{6} is unity and it has extrema at x = - 1 and x = 1 . If lim x \to 0 \frac{f ( x )}{x ^{3}} = 1, then 5. f (2) is equal to$

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