Match List – I with List – II.
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LIST I |
LIST II |
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A. If $y=x^4+5 x^2+3$, then $\frac{d^2 y}{d x^2}$ is, |
I. $12 x$ |
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B. If $y=2 x^3+6 x+5$, then $\frac{d^2 y}{d x^2}$ is, |
II. $\frac{1}{x}$ |
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C. If $y=x \log x$, then $\frac{d^2 y}{d x^2}$ is, |
III. 0 |
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D. If $y=2 x+1$, then $\frac{d^2 y}{d x^2}$ is, |
IV. $12 x^2+10$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-IV, B-I, C-II, D-III
$\text{A: } y = x^4 + 5x^2 + 3$
$y' = 4x^3 + 10x,\quad y'' = 12x^2 + 10 \Rightarrow \text{IV}$
$\text{B: } y = 2x^3 + 6x + 5$
$y' = 6x^2 + 6,\quad y'' = 12x \Rightarrow \text{I}$
$\text{C: } y = x\log x$
$y' = \log x + 1,\quad y'' = \frac{1}{x} \Rightarrow \text{II}$
$\text{D: } y = 2x + 1$
$y'' = 0 \Rightarrow \text{III}$
$\text{A-IV,\ B-I,\ C-II,\ D-III}$