What is the smallest distance of y = cos(x) + 1 to the origin using IVT and RT?

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Using IVT and RT, work out an estimate for the smallest distance of the curve y = cos(x) + 1 to the origin

i know intermediate value and rolle's theorem , but i don't know how to tackle this problem do you have any idea ?
 
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Try using the Pythagorean theorem and treat this like an optimization problem.
 

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