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Calculus

Quick questions on Tangents, normals and rates of change 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 is the tangent line?
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The derivative dydx\dfrac{dy}{dx} evaluated at a point gives the gradient of the tangent there. The tangent equation follows from the point-gradient form:
What is the normal line?
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The normal is perpendicular to the tangent, so its gradient is the negative reciprocal −1m-\dfrac{1}{m} (provided m≠0m \neq 0). Use the same point with this gradient.
What is connected rates of change?
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When two quantities are related and both change with time, their rates link through the chain rule:
What is q1?
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Find the tangent to y=1xy = \dfrac{1}{x} at (1,1)(1, 1). [3 marks]
What is q2?
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State the gradient of the normal if the tangent gradient is 23\frac{2}{3}. [1 mark]
What is q3?
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The side of a square increases at 2 cm s−12\ \text{cm s}^{-1}. Find the rate of increase of the area when the side is 5 cm5\ \text{cm}. [3 marks]

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