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JAMB Mathematics 2019 Paper

Question : 71

Total: 73

If y = 8x

{}^3

{}^2

\frac{d^2 y}{d x^2}

Solution:

Concept:

The second derivative is found by differentiating the given function twice.

Explanation:

Start with the function

y = 8x^{3} - 3x^{2} + 7x - 1

Find the first derivative using the power rule:

\frac{d}{dx}(x^n) = nx^{n-1}

\frac{dy}{dx} = 3 \times 8x^{3-1} - 2 \times 3x^{2-1} + 1 \times 7x^{1-1} - 0

\frac{dy}{dx} = 24x^{2} - 6x + 7

Now differentiate

\frac{dy}{dx}

to obtain the second derivative.

\frac{d^2 y}{dx^2} = \frac{d}{dx}(24x^{2} - 6x + 7)

\frac{d^2 y}{dx^2} = 2 \times 24x^{2-1} - 1 \times 6x^{1-1} + 0

\frac{d^2 y}{dx^2} = 48x - 6

Answer:

\frac{d^2 y}{dx^2} = 48x - 6

The correct option is A.

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