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Broad Topics > Pre-Calculus and Calculus > Quotient rule

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Exponential Trend

Age 16 to 18 Challenge Level:

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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Bird-brained

Age 16 to 18 Challenge Level:

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

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Weekly Challenge 42: What's My Equation?

Age 16 to 18 Challenge Level:

Can you find the differential equations giving rise to these famous solutions?