Given 2 real numbers whose sum is 14. find the minimum possible value for the sum of their squares (answer is an integer or a reduced fraction; NO GUESSING)

Question

anonymous · Answer

x+y=14

x^2+y^2=  __

2nd equation is the one we want to minimize

substituting first equation into 2nd equation

x^2+ (14-x)^2 = ___

take the 2nd equation and find the first derivative and set it equal to zero

then solve for x
then solve for y

then plug back into 2nd original equation to determine lowest value

anonymous · Answer

Can you be more descriptive with the last part, starting from setting it to zero

anonymous · Answer

|dw:1368838728748:dw|

assume that the function for the 2nd equation looks something like that

anonymous · Answer

we want to find the lowest point|dw:1368838787499:dw|
this can be done by taking the first derivative of the of the 2nd equation and setting it equal to zero

the first derivative gives you an equation for the slope of the line at any point of the graph

so at the lowest point of the graph, the slope  is equal to zero

so taking the first derivative of the 2nd equation with respect to x and setting it equal to zero gives us a solveable equation

anonymous · Answer

so when you take first derivative and set it equal to zero
you will get something that looks like

2x-28+2x =0

so solve for x and that will give you the x value at the lowest value

anonymous · Answer

Refer to the attached Mathematica solution: