Maximum of a vector field

Question

Lets say a vector field represents the speed of a river

$$F = (-x/20, 20 - x^2 / 1000)\quad 100 \le x \le 100$$

Find the $x$ and $y$ values of the maximum speed in the river.

The norm of the feild yeilds the length of a vector at any (x, y).

|F| = (x^4 - 37500x^2 + 400000000)^1/2 / 1000

the solution is (0, 20) because at x = 0 |F| is horizontal and a maximum.

Maximize this function.

Answer 1

HINT

We have that for $F=(F_x,F_y)$

$$|F|=\sqrt{F_x^2+F_y^2}$$