Weekly Challenge 25: Trig Trig Trig
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'.