Page:Calculus Made Easy.pdf/139

 (4) Find the maxima and minima of

(5) Find the maxima and minima of

(6) Find the maxima and minima of

(7) Find the maxima and minima of

(8) Divide a number $$N$$ into two parts in such a way that three times the square of one part plus twice the square of the other part shall be a minimum.

(9) The efficiency $$u$$ of an electric generator at different values of output $$x$$ is expressed by the general equation:

where $$a$$ is a constant depending chiefly on the energy losses in the iron and $$c$$ a constant depending chiefly on the resistance of the copper parts. Find an expression for that value of the output at which the efficiency will be a maximum.