Question

The sum of two nonnegative numbers is 36. Find these numbers if the first plus the square of the second is a maximum.

Answer 1

Set up an equation. What are you given?

Answer 2

that's all the information i was given and i have no idea what to do! :(

Answer 3

Hero: it should be:\[x+y=36\]

Answer 4

x + y = 36 (duh)
x + y^2 = maximum

(Wondering how to figure out the maximum)

Answer 5

can someone please help me figure out the answer

Answer 6

is this calculus?

Answer 7

yes it is

Answer 8

Yeah, this definitely would involve calculus. Taking a derivative would help.

Answer 9

m = x + (36 - x)^2

Answer 10

express the second equation in terms of x, then set the derivative equal to zero

Answer 11

x+y=36
x+y^2 = maximum

it can be inferred by ituition that y=36 and x= 0 gives the maximum, although for a rigorous proof
replace x in terms of y, get
y^2-y+36

upward opening parabola, no local maxima exists, hence we take the largest value in the domain, which is y=36.

hence the solution is x=0 and y=36

Answer 12

setting the derivative as zero will give minima and not maxima @TuringTest

Answer 13

would it be 6 instead of 36 since a number has to be squared and 6 squared is 36?

Answer 14

setting the derivative equal to zero will give any extrema, max or min @Stom

Answer 15

its 36 and not 6 , as the question says that sum of those 2 nimbers is 36, @turingtest
ya,

Answer 16

...so in this case, the maximum occurred at one of the endpoints
when looking for an absolute max or min, you must check all extrema (i.e. when the derivative equals zero) as well as the endpoints of the possible intervals. In this case x=0 y=36 and x=36 y=0 are the endpoints