A man stands at a point A on the bank of a straight river, 2 miles wide. To reach point B, 7 miles downstream?

on the opposite bank, he first rows his boat to point P on the opposite bank and then walks the remaining distance x to B. He can row at 2 mi/hr and walk 5 mi/hr. Where should he land so that he reaches B as soon as possible?

f(x) =sqrt(2^2 +x^2)/2 +(7-x)/5

=sqrt(4+x^2)/2 +7/5 -x/5

Now find f'(x) and set =0, solve for x.

Set there is an opposite point C at another side of the river to the point A

and the man should land at the point D, which is one point between A and B

so, the time cost is (x+2)^0.5/2+(7-x)/5

calculate the derivative

1/4(x+2)^2-1/5=0

we get x=-7/16 is nagitive

so the man should directly land at the opposite point C