Match List-I with List-II.
| List-I | List-II | ||
| (A) | If $y=x^2-8$ and $\frac{dy}{dx}=0, $ then $x= ?$ | (I) | 1 |
| (B) | If $p(x)=3x+1, $ then $R(x)$ at x = 2 | (II) | 0 |
| (C) |
If $y= x^3,$ then $\frac{dy}{dx}$ at $x=-1 $ |
(III) | 14 |
| (D) | If $C(x)=100+ 5x, R(x)=102+3x,$ then breakeven point | (IV) | 3 |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) -(II), (B)- (III), (C) -(IV), (D) -(I)
(A) $y=x^2-8$
$⇒\frac{dy}{dx}=2x=0$
$⇒x=0$ (II)
(B) $P(x)=3x+1$
$R(x)=x.P(x)$
$=3x^2+x$
$R(2)=3(2)^2+2=14$ (III)
(C) $y=x^3$
$⇒\frac{dy}{dx}=3x^2$
$⇒\left.\frac{dy}{dx}\right]_{x=-1}=3(-1)^2=3$ (IV)
(D) $C(x)=100+5x,R(x)=102+3x$
$⇒R(x)=C(x)$
$⇒100+5x=102+3x$
$⇒2x=2$
$⇒x=1$ (I)