Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x=–1 and x=1. If limx→0f(x)x3=1 then 5.f(2) is equal to
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Solution
f(x)=x6+ax5+bx4+x3 ∴f′(x)=6x5+5ax4+4bx3+3x2 Roots are 1 and −1 ∴6+5a+4b+3=0 & −6+5a−4b+3=0 solving a=−35b=−32 ∴f(x)=x6−35x5−32x4+x3 ∴5.f(2)=5[64−965−24+8]=144