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Find the coordinate location of the minimum turning point for the structural profile function curve y = x²-4x +3.
The structural strength S of a timber beam variant is approximated by the relationship equation S(x) = x(12 – x) = 12x – x², where x represents the beam width in centimeters. Find the width that maximizes the beam's overall structural strength capacity.
Use the chain rule to find the derivative of the composite trigonometric function y cos(4x³) .
