In a financial mathematics, investors use utility functions to compare the "joy" of earning money on an investment

to the "pain" of losing money on the same investment. Suppose that an investor using the utility u=w^1/2 has 10000 and is trying to determine how much of this amount to invest in a stock (i .e. $1000x where 0 is less than equal to x less than equal to 1). Assuming that

when $10000x is invested there is 75% chance it is won (i.e. doubled) and a 25% chance it is lost entirely ; then the expected utility can be shown to be: y = 0.75((10000 +10000x)^1/2) +0.25(10000-10000x)^1/2

Use the closed interval method/EV to determine the percentage x of the investor's $10000 that they should invest in order to maximize their expected utility y (i.e. maximize their expected "joy" of winning over "pain" of losing).