If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so that the product of the first and cube of the second is a maximum.

If we translate the word problems to mathematical equation,
 
                             2x + 3y = 60

The second equation is,
 
                            P = xy³

From the first equation, we get the value of y in terms of x.
  
                             y = (60 - 2x) / 3

Then, substitute the expression of y to the second equation,
 
                            P = x (60-2x) / 3
                            P = (60x - 2x²) / 3 = 20x - 2x²/3

We derive the equation and equate the derivative to zero.

                           dP/dx = 0 = 20 - 4x/3

The value of x from the equation is 15.

Hence, the value of x for the value of the second expression to be maximum is equal to 15. 
                               

It would be the second one because it passes the vertical line test

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.