240 



EXAMPLES OF MAXIMA AND MINIMA. 



5. To find a point such that the sum of the straight lines 

 joining it with the angular points of a given triangle shall be 

 a minimum. 



Let ABC be the given triangle; let BC=a, CA-l, 

 AB = c. Take any point P 

 and draw PM perpendicular 

 to AB; let A M = x, PM= y. 

 Also let AP=u, BP = v, 

 CP=w; the angle APM= 6, 



Then M 2 



rti i /* _^ _ nr*\ J- 97 

 t/ \ O ^^ t*/ I T^ w A 



\ / 7 * - >- 



w 2 = (ft cos J. - a;) 1 + (ft sin A - y}\ 

 For a minimum value of u + v + w we must have 



/IN 



