Question

find two numbers whose product is 64 , and whose sum is a minimim

Answer 1

calculus question, right ?
do u know how to take derivatives ?

Answer 2

yes, but i don know how to form an equation

Answer 3

Ab = 64

Their sum is a minimum.

So, the sum S of a and b, S = a + b should be minimum.

To get the minimum, you have to find the derivative of S (or find the shape of the graph of S as a and b vary.

S = a + b

Substitute either a = 64/b or b = 64/a. I'll do the second.

S = a + 64/a

Now, you can find the derivative of that equation, equate to zero and solve for a, the first number.

Then use the first equation to get the value of b.

Answer 4

let 2 numbers be x andy
xy=64
sum = f(x) = x+y = x+64/x
now minimise f(x)

Answer 5

am i going to derive x + 64/x?

Answer 6

yup.
cun u ?

Answer 7

*can

Answer 8

1 + 64?

Answer 9

nopes, what is the derivative of 1/x ??

Answer 10

sorry,
1 - 64/x2

Answer 11

now equate that to 0

Answer 12

(x^2 - 64)/x^2 = 0

Answer 13

so numerator = 0

Answer 14

why?

Answer 15

if a/b=0 then a=0.
(multiplying b on both sides)

Answer 16

so here u get x^2-64=0

Answer 17

yew, then i will transpose -64 to the right side?

Answer 18

yup.
then take square root.

Answer 19

for your reference.
x^2=64
x=8 or x=-8
x cannot be 8 because the 2nd derivative becomes negative and u get a maxima.
x=-8 is correct because 2nd derivative is positive and u get a minima.
so 2 numbers are
-8 and 64/(-8) = -8
whose sum = -8-8 = -16