Question 1179760
Let one number x and the other one y.
 
x + y = 29
 
The product of the two numbers will be x * y = xy
 
solve x + y = 29 
 
y = 29 - x
 
x * y = x(29 - x) = 29x - x²
 
 let f(x)= 29x-x^2, 
 f'(x) = 29 - 2x
 
The maximum value of this function will occur at a critical number. A critical number occurs where f'(x) = 0 or is undefined.
 
f'(x) is defined for all real x.
 
We only need to determine where f'(x) = 0
 
29 - 2x = 0
 
29 = 2x
 
x = 14.5
 
The two numbers are 14.5 ,14.5 The maximum product is 210.5.