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If y = 3x3 - 5x2 + 2 then \(\rm \frac {d^2 y}{dx^2}\) =
1. 18x + 10
2. 18x - 10
3. 9x + 5
4. 9x - 5

1 Answer

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Best answer
Correct Answer - Option 2 : 18x - 10

Concept:

Second-order Derivative.

\(\rm \frac {d^2 f(x)}{dx^2} = \) \(\rm \frac {d}{dx} [\frac {d}{dx} f(x)]\)

\(\rm \frac {d}{dx}e^{f(x)} = e^{f(x)} f'(x)\)

Calculations:

y = 3x3 - 5x2​ + 2 

Differentiating w.r. to x on both side, we get

\(\rm \dfrac {dy}{dx}\) = (3 × 3x2) - (5 × 2x) + 0

⇒ 9x2 - 10x

Again Differentiating w.r. to x on both sides, we get 

\(\rm \dfrac {d^2y}{{dx}^2}\) = (9 × 2x) - 10

\(⇒\rm \dfrac {d^2y}{{dx}^2} = 18x - 10\)

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