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Calculus

Quick questions on Implicit and parametric differentiation explained: H2 Mathematics Calculus

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are second derivatives?
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For a parametric curve the second derivative is not the second tt-derivative ratio; it is
What are tangents?
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Once you have dydx\dfrac{dy}{dx} at a point, the tangent uses the usual point-gradient form. Horizontal tangents occur where the numerator of dydx\dfrac{dy}{dx} is zero; vertical tangents where the denominator is zero.
What is wrong product rule on a mixed term?
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ddx(xy)=y+xdydx\dfrac{d}{dx}(xy) = y + x\dfrac{dy}{dx}; both terms are needed.
What is q1?
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Find dydx\dfrac{dy}{dx} for x2+y2=16x^2 + y^2 = 16. [2 marks]
What is q2?
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A curve has x=t2x = t^2, y=2ty = 2t. Find dydx\dfrac{dy}{dx} in terms of tt. [2 marks]
What is q3?
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State how to find a vertical tangent on a parametric curve. [1 mark]

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