This positive number is 1/2. First we construct an equation that represents what is being described, with x being our number to find:
y = 1/x + 4*x^2
Take the derivative:
y’ = -1/(x^2) + 8x
Our number would be the value of x where the derivative of y = 0:
0 = -1/(x^2) + 8x
Solve for x:
1/(x^2) = 8x
1 = 8x^3
1/8 = x^3
x = 1/2
