William Anthony Granville

“ It is desired to make an open-top box of greatest possible volume from a square piece of tin whose side is a, by cutting equal squares out of the corners and then folding up the tin to form the sides. ”

“ Open-top box. which is the function to be made a maximum by varying x. Applying rule,
First step. .
Second step. Solving gives critical values and .
It is evident from the figure that must give a minimum, for then all the tin would be cut away, leaving no material out of which to make a box. By the usual test, is found to give a maximum volume . Hence the side of the square to be cut out is one sixth of the side of the given square. ”

“ A steel girder 25 ft. long is moved on rollers along a passageway 12.8 ft. wide and into a corridor at right angles to the passageway. Neglecting the width of the girder, how wide must the corridor be? ”

“ Ans. = 45°. 65. The total time of flight of the projectile in the last problem is given by the formula
. At what angle should it be projected in order to make the time of flight a maximum?
Ans. = 90°. 66. The time it takes a ball to roll down an inclined plane AB is given by the formula.
Inclined plane AB. . Neglecting friction, etc., what must be the value of to make the quickest descent?
Ans. °. 67. Examine the function for maximum and minimum values. Use the first method, p. 111.
When . When . Therefore, when x = 1 the function has a minimum value (= ordinate of C) . ”