Question

The product of two numbers is 192. what is the minimum value of the sum of the first value plus twice the second value

Answer 1

Let x and y be the two positive numbers. -  Their product is 192: x *  y  =  192   equation 1

-  the sum of the first plus twice the second is a minimum:  x + 2y

From the first equation, y =  192 / x. 
Substitute that into the second equation:

 x + 2y = x + 2(192/x ) = x + 384/x

f(x) is minimum when f'(x) = 0 and f"(x) > 0 

f(x)= x + 384/x

f(x) = 1-384/x^2 

1-384  / x^2 =  0 

x^2-384 = 0 

x^ 2= 354
 x = radical  354    = 18.8  here i'm confused why the number is decimal
???/