The sum of two positive numbers is 12. what two numbers will maximize the product g

Given two numbers x and y such that:

x + y = 12   ...    (1)

from  equation (1) 

y = 12 - x  

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

 f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

 2x =  12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

  4 + 22x − 1 = 0

Step-by-step explanation:

Start off with the standard formula to finding area with polynomials and quadratic functions.

(2x + 5)(2x + 6)

Work out like a normal binomial.

4 + 22x + 30 - 31

(You're subtracting 31 to take out the minimum of what the frame has to be)

4 + 22x - 1 = 0