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Let a ,b inRR be such that the function ...

Let a ,b `inRR` be such that the function f given by `f(x)=log|x|+bx^(2)+ax,xne0`
Statement - I : f has local maximum at x=-1 and x=2.
Statement - II : f'' `(-1)lt0and` also `f''(2)lt0`

A

Statement - I is true , Statement - II is true , Statement -II is a correct explanation for Statement - I

B

Statement - I is True , Statement - II is True , Statement -II is not a correct explanation for Statement - I

C

Statement - I is True , Statement - II is False.

D

Statement - I is False , Statement - II is False.

Text Solution

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The correct Answer is:
A
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a, b in RR be such that the function f given by f(x)=ln|x|+bx^(2)+ax,xne0 has extreme values at x=-1 and x = 2. Statement-I : f has local maximum at x = -1 and at x = 2. Statement-II : a=(1)/(2)" and "b=-(1)/(4) .

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Knowledge Check

  • Let a, binR be such that the function f given by f(x)=ln|x|+bx^2+ax,xne0 has extreme values at x = -1 and x = 2 Statement 1:f has local maximum ar x=-1 and x=2. Statement 2: a=1/2 and b=1/4

    A
    Statement 1 is false, Statement 2 is true.
    B
    Statement 1 is true , Statement 2 is true , Statement 2 is a correct explanation for Statemen
    C
    Statement 1 is true, Statement 2 is true , Statement 2 is not a correct explanation for Statement 1
    D
    Statement 1 is true, Statement 2 is false.

  • Let f(x)=2x^(3)+3x^(2)-12 x+1 . Statement - I : f decreases on (-2, 1). Statement - II : The solution set of x^(2)+x-2 lt 0 is (-2, 1).

    A
    Satement -I is True, Statement -II is True, Statement -II is a correct explanation for Statement -I
    B
    Satement -I is True, Statement -II is True, Statement -II is not a correct explanation for Statement -I
    C
    Stament -I is True, Statement -II is False.
    D
    Statement -I is False, Statement -II is True.

  • Statement - I : If f(x) = sinx, then f'(0) = f'(2pi) Statement - II : If f(x) = sin x , then f(0) =f(2pi) .

    A
    Statement - I is true , Statement - II is true , Statement -II is a correct explanation for Statement - I
    B
    Statement - I is True , Statement - II is True , Statement -II is not a correct explanation for Statement - I
    C
    Statement - I is True , Satement - II is False.
    D
    Statement - I is true , Statement - II is true , Statement -II is a correct explanation for Statement - I

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