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A Close Match
Can you massage the parameters of these curves to make them match as closely as possible?
Age 16 to 18 Short
Challenge Level
Consider the function $f(x)=\cos(\sin(\cos(x)))$, with $x$ measured in radians.
What turning points can you find?
What are the maximum and minimum values of the function?
Did you know ... ?
This function is bounded, continuous and differentiable at all points. Mathematicians often use knowledge of conditions such as these to deduce lots of information about the properties of functions without the need for extensive calculation. In first year undergraduate analysis courses theorems are rigorously stated and proved which support intuitive statements such as 'between any two maxima a minimum must be found if the function is finite, continuous and differentiable'.
This function is bounded, continuous and differentiable at all points. Mathematicians often use knowledge of conditions such as these to deduce lots of information about the properties of functions without the need for extensive calculation. In first year undergraduate analysis courses theorems are rigorously stated and proved which support intuitive statements such as 'between any two maxima a minimum must be found if the function is finite, continuous and differentiable'.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.