Match List-I with List-II
|
List-I Function |
List-II Increasing on the interval |
|
(A) $f(x)=-x^2-2x+1$ |
(I) $(-∞,-1)$ |
|
(B) $f(x) = x^2+1$ |
(II) $(1,∞)$ |
|
(C) $f(x) = x^2-2x+3$ |
(III) $(-∞,0)$ |
|
(D) $f(x) = -x^2$ |
(IV) $(0,∞)$ |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(I), (B)-(IV), (C)-(II), (D)-(III) **
|
List-I Function |
List-II Increasing on the interval |
|
(A) $f(x)=-x^2-2x+1$ |
(I) $(-∞,-1)$ |
|
(B) $f(x) = x^2+1$ |
(IV) $(0,∞)$ |
|
(C) $f(x) = x^2-2x+3$ |
(II) $(1,∞)$ |
|
(D) $f(x) = -x^2$ |
(III) $(-∞,0)$ |
(A) $f(x)=-x^2-2x+1$
$f'(x)= -2x - 2$
Increasing when $-2x-2>0 \Rightarrow x<-1$
Matches (I)
(B) $f(x)=x^2+1$
$f'(x)=2x$
Increasing when $x>0$
Matches (IV)
(C) $f(x)=x^2-2x+3$
$f'(x)=2x-2$
Increasing when $x>1$
Matches (II)
(D) $f(x)=-x^2$
$f'(x)=-2x$
Increasing when $x<0$
Matches (III)