Quick questions on Stationary points and their nature: N(A)-Level Additional Mathematics

5short 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 classifying with the second derivative?

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The fastest test is the second derivative

\dfrac{d^2y}{dx^2}

, found by differentiating again. At a stationary point:

What is classifying with a sign test?

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Alternatively, check the sign of

\dfrac{dy}{dx}

just before and just after the point:

What is q1?

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Find the

x

-coordinate of the stationary point of

y = x^2 - 10x

. [2 marks]

What is q2?

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A curve has

\dfrac{d^2y}{dx^2} = -4

at its stationary point. State its nature. [1 mark]

What is q3?

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Find the stationary point of

y = x^2 + 2x + 3

and state its nature. [3 marks]

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