Thread: Solve a problem using derivatives.

1. Solve a problem using derivatives.

A person is in a small boat in the point A on one side of a lake parallel shores. He will move from A to point B on the lake's other side as shown. The total time for transfer is assumed to be y s. He paddles 3 m/s and run 5 m/s.
a) express y as a function of x (see figure).
b) examine graphically whether he can cope with the movement in 2 min.
c) determination by differentiation the shortest time to transfer.

2. -deleted-

3. Originally Posted by hejmh
A person is in a small boat in the point A on one side of a lake parallel shores. He will move from A to point B on the lake's other side as shown. The total time for transfer is assumed to be y s. He paddles 3 m/s and run 5 m/s.
a) express y as a function of x (see figure).
b) examine graphically whether he can cope with the movement in 2 min.
c) determination by differentiation the shortest time to transfer.

a) $\displaystyle y=\frac{270-x}{5}+\frac{\sqrt{x^2+300^2}}{3}$