Parametric Equations: Second Derivative Calculation

00:00 4 marks

Given the parametric equations \(x(t)=t^2+1\) and \(y(t)=t^3-3t\), find the second derivative \(\frac{d^2y}{dx^2}\) at the point corresponding to \(t=2\).

Recall that the second derivative for parametric equations is given by \(\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}\).

Hint Hint

Hint

First compute \(\frac{dy}{dt}\) and \(\frac{dx}{dt}\) to find \(\frac{dy}{dx}\), then differentiate again using the chain rule.

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\(\frac{15}{32}\)

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Parametric Equations: Second Derivative Calculation

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Parametric Equations: Second Derivative Calculation

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