Steel Magnolias. Steel is made up of iron, carbon and sometimes other elements s

Question

Steel Magnolias. Steel is made up of iron, carbon and sometimes other elements such as manganese, chromium, and nickel. The tensile strength of a steel will depend on the amount of carbon in it. A graph of the tensile strength of a particular type of steel as a function of the percent of carbon is graphed below. Carbon The equation of this curve is Y = 76 + 2160X -600X^2, where Y = the tensile strength of the steel and X is the percent of carbon in the steel. Find the carbon level that maximizes the strength of the steel.

Explanation / Answer

y =76+ 2160x -600x2

tensile strength is maximised when dy/dx =0 ,d2y/dx2<0

dy/dx =0+ 2160 -1200x =0

=>x =2160/1200

=>x =1.8

d2y/dx2 = -1200<0

so 1.8% carbon lel maximises strength of steel

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