I have a question that is as follows..
Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead (One possible explanation is the fact that extra energy is required to fly over water). Assume a pigeon is released from a boat 1 mile from the shore of a lake (Point B), flies first to point P on the short and then along the straight edge of the lake to reach its home at L. If L is 2 miles from point A, the point on the shore closest to the boat, and if a pigeon needs 4/3 as much energy per mile to fly over water as over land, find the location of point P, which minimizes energy used.
So Obviously I need to find the absolute minimum, and to do this, I need to create a function, differentiate it, find the critical number and then plug that into the formula to find the extrema.
I don't know if I'm setting the function up correctly though, and I'm also having a bit of trouble differentiating the function I do have set up.
That's an image of my working, though I don't think its correct, because the final value I Get can not be correct..