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Quick questions on Differentiation: rules, stationary points and optimisation - Edexcel A-Level Maths

4short 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 stationary points?
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A stationary point occurs where dydx=0\dfrac{dy}{dx} = 0. Classify it with the second derivative: d2ydx2>0\dfrac{d^2y}{dx^2} > 0 means a minimum, d2ydx2<0\dfrac{d^2y}{dx^2} < 0 means a maximum, and if it is zero you must test the sign of the first derivative either side.
What is not checking the nature of an optimisation solution?
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Always confirm you have a maximum or minimum as required.
What is q1?
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Differentiate y=(2x+1)4y = (2x + 1)^4. [2 marks]
What is q2?
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Find the maximum value of y=12x−x3y = 12x - x^3 for x>0x > 0. [4 marks]

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