Hey guys

Sorry ...here's another differentiation problem i can't solve ><" ...i asked my friends but they have no clue and since it's the holz my teacher is inaccessible

Although an example in the textbook showed a similar question, i can't seem to get the answer with the method shown.

Problem: A man in a boat is 4 km from the nearest point O of a straight beach; his destination is 4 km along the beach from O. If he can row at 4 m/h and walk at 5 km/h, how should he proceed in order toreach his destination in the least possible time?

The textbook answer is: Row direct to destination.

Here's my solution:

$\displaystyle 4^2 + x^2 = BC$(Pythagoras' Theorem)

$\displaystyle BC = \sqrt{16 + x^2}$

Time to travel BC $\displaystyle = \frac{\sqrt{16 + x^2}}{4}$

Time to travel CD$\displaystyle = \frac{4-x}{5}$

Total time T$\displaystyle = \frac{\sqrt{16 + x^2}}{4} + \frac{4-x}{5}$

$\displaystyle \frac{dT}{dx} = \frac{x\sqrt{16 + x^2}}{4} - \frac{3}{50}$

For least possible time, $\displaystyle \frac{dT}{dx} = 0$

......

When I work out x, it equals approx. 0.06...which does not make sense at all.

Please help?