Re: Much quoted calculus problem

On Wed, 06 Sep 2006 06:19:45 -0700, mitch wrote:

Hi,

I'd be very interested in people's help in interpreting this problems
solution:

A man is in a boat D1 kilometres from the nearest point A of a straight
coast.

He wishes to reach point B on the coast which is D2 kilometres from A
in the shortest possible time.

If he can row at V1 kilometres per hour and run at V2 kilometres per
hour,how far from A should he land? (call this distance x kilometres)

snip>
Mitch.
When looking for a minimum you should always look not only for critical
points (where the derivative is 0), but also the endpoints, if any (in
this there are none), and any points at which the objective function is
not differentiable. The time taken if the man lands x along the shore from
A is sqrt( D1*D1 + x*x)/V1 + |(D2-x)/V2|
Note the absolute value!
This is not differentiable at x=D2. So in this case you you should
evaluate the function at the critical point and at x=D2.
Duncan

.

Relevant Pages

  • Re: Much quoted calculus problem
    ... A man is in a boat D1 kilometres from the nearest point A of a straight ... Any spot further should be done on land from x and further. ... entirely by water, as B will be finite, and so less than x. ...
    (sci.math)
  • Much quoted calculus problem
    ... A man is in a boat D1 kilometres from the nearest point A of a straight ... He wishes to reach point B on the coast which is D2 kilometres from A ...
    (sci.math)