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CURVATURE OF CURVES

119

(4) Find the maxima and minima of

$y=2x+1+{\frac {5}{x^{2}}}$ .

(5) Find the maxima and minima of

$y={\frac {3}{x^{2}+x+1}}$ .

(6) Find the maxima and minima of

$y={\frac {5x}{2+x^{2}}}$ .

(7) Find the maxima and minima of

$y={\frac {3x}{x^{2}-3}}+{\frac {x}{2}}+5$ .

(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:

$u={\frac {x}{a+bx+cx^{2}}}$ ;

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.

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