The function f(x)=x^3-6x^2+ax+b is such that f(2) = f(4) = 0. Consider two statements. (S_1) there exists...

Question

The function f(x)=x^3-6x^2+ax+b is such that f(2) = f(4) = 0. Consider two statements. (S_1) there exists x_1, x_2 (2,4), x_1<x_2, such that f'(x_1)=–1 and f'(x_2)=0. (S_2) there exists x_3,x_4 (2,4), x_3<x_4, such that f is decreasing in (2,x_4), increasing in (x_4,4) and 2f'(x_3)= 3f(x_4). Then

Accepted Answer

(A)

JEE Main 2021 Mathematics question

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