Deflections of diving boards A diver stands at the very end of a diving board before begin...

Deflections of diving boards A diver stands at the very end of a diving board before beginning a dive. The deflection d of the board at a position s feet from the stationary end is given by d =cs2(3L −s) for 0 ≤ s ≤L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physical properties of the board (see the figure). Suppose the board is 10 feet long.

EXERCISE

(a) If the deflection at the end of the board is 1 foot, find c.

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(b) Show that the deflection is 2 foot somewhere between s =6.5 and s =6.6.