+866 Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.
+128578 6x + (3/5)y
xy = 2/5
y = 2 /(5x)
6x + (3/5)(2) / (5x)
6x + (6/25)x^(-1) take the derivative and set to 0
6 - (6/25)x^(-2) = 0 multiply
6x^2 = (6/25)
x^2 = 1/25
x = 1/5
Take the scond derivative to see that this is a min
2(6/25)(.2)^(-3) = 60 which is > 0 ....so this is a min
Min at (.2, 2) = 6(.2) + (3/5)(2) = 1.2 + 1.2 = 2.4
