Consider the function $f(x)=x^3-3x$. Then
Match List-I with List-II
|
List-I |
List-II |
|
(A) Point of local Maxima |
(I) 1 |
|
(B) Point of local Minima |
(II) -1 |
|
(C) Local maximum value |
(III) 2 |
|
(D) Local minimum value |
(IV) -2 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
|
List-I |
List-II |
|
(A) Point of local Maxima |
(II) -1 |
|
(B) Point of local Minima |
(I) 1 |
|
(C) Local maximum value |
(III) 2 |
|
(D) Local minimum value |
(IV) -2 |
Given
$f(x)=x^3-3x$
$f'(x)=3x^2-3=3(x^2-1)$
Critical points from $f'(x)=0$
$x^2-1=0$
$x=1,-1$
$f''(x)=6x$
$f''(-1)=-6<0$ so $x=-1$ is point of local maxima
$f''(1)=6>0$ so $x=1$ is point of local minima
Local maximum value
$f(-1)=(-1)^3-3(-1)=-1+3=2$
Local minimum value
$f(1)=1-3=-2$
Correct matching: A-II, B-I, C-III, D-IV.