Page:Calculus Made Easy.pdf/140

 (10) Suppose it to be known that consumption of coal by a certain steamer may be represented by the formula $$y=0.3+0.001v^3$$; where $$y$$ is the number of tons of coal burned per hour and $$v$$ is the speed expressed in nautical miles per hour. The cost of wages, interest on capital, and depreciation of that ship are together equal, per hour, to the cost of $$1$$ ton of coal. What speed will make the total cost of a voyage of $$1000$$ nautical miles a minimum? And, if coal costs $$10$$ shillings per ton, what will that minimum cost of the voyage amount to?

(11) Find the maxima and minima of $y=\pm\frac{x}{6} \sqrt{x(10-x)}$.

(12) Find the maxima and minima of $y=4x^3-x^2-2x+1.$