Question

Find the maximum value of the product of two numbers x and x-10 which add up to 10.

Answer 1

5 by pure reason

Answer 2

so how did you calcutlate it?

Answer 3

i assume you mean x and 10 - x since they add to ten. each number is five and the product is 25

Answer 4

oh yea, thats right! thanks for your help mate :)

Answer 5

yw

Answer 6

if you have to write something for your teacher, write
the product is
\[x(10-x)=10x-x^2\] which will have a maximum value at the vertex which is
\[-\frac{b}{2a}=\frac{10}{2}=5\]

Answer 7

okay, but how did you get the second part?

Answer 8

5 is the x coordinate of the vertex. To get the y coordinate plug x into 10x - x^2

Answer 9

okay, so a=1 and b=10? do you just ignore the negative?

Answer 10

no because
\[a=-1\] and there is a -1 in the 'formula' which is why it is postive

Answer 11

anyway to heck with the formula. you have two numbers and this setup is completely symmetric, but which i mean you cannot tell the numbers apart. x and 10 - x or 10 - x and x
so clearly it is the biggest when they are the same

Answer 12

oh i see! that makes sense now, thankss! sorry to irritate you lol

Answer 13

no irritation, no problem. i only wrote that vertex thing in case you had to hand something in to your teacher