Question

Question #b08a5

Answer 1

Lets let our two numbers be `a` and `b`. The problem tells us that;

`a + b = 9`
`a xx b^2 =`max

We want to combine these two pieces of information to get one function with one variable. We can rearrange the first equation to solve for `a`.

`a = 9-b`

Plug this into the second.

`(9-b) xx b^2`
`=9b^2-b^3`

Now we take the derivative and set it equal to zero to find our optimized value of `b`. The power rule gives us;

`18b-3b^2=0`
`3b = 18`
`b=6`

Using the first equation, we can find that `a` must equal `3`, so our two numbers are `3` and `6`.