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

$y=4x^{3}-x^{2}-2x+1.$