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Application of Derivatives question

2021 · 1 Sep · Shift 2 · Q29
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  5. /2021 · 1 Sep · Shift 2 · Q29

Application of Derivatives question

2021 · 1 Sep · Shift 2 · Q29

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1
The function f(x)=x3−6x2+ax+bf(x) = {x^3} - 6{x^2} + ax + bf(x)=x3−6x2+ax+b is such that f(2)=f(4)=0f(2) = f(4) = 0f(2)=f(4)=0. Consider two statements : Statement 1 : there exists x1, x2 ∈\in∈(2, 4), x1 < x2, such that f'(x1) = −-− 1 and f'(x2) = 0. Statement 2 : there exists x3, x4 ∈\in∈(2, 4), x3 < x4, such that f is decreasing in (2, x4), increasing in (x4, 4) and 2f′(x3)=3f(x4)2f'({x_3}) = \sqrt 3 f({x_4})2f′(x3​)=3​f(x4​). Then
  1. A
    both Statement 1 and Statement 2 are true
  2. B
    Statement 1 is false and Statement 2 is true
  3. C
    both Statement 1 and Statement 2 are false
  4. D
    Statement 1 is true and Statement 2 is false
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