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Calculus Countdown

Age 16 to 18
Challenge Level Yellow star
  • Problem
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To begin with, try acting on the starting functions with various operators to see the sorts of possibilities that occur.

To hit a target, think what functions would be needed to make them in one step. How might I arrive at these inputs?

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Generally Geometric

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

Bend

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Exponential Trend

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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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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