Question

The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees celsius) is modeled by: p(x)=-2(x-9)^2+200, what is the maximum number of fish?

Answer 1

The maximum number of fish is going to be p(9) = 200

Answer 2

Explanation:

Given that the fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees celsius) is modeled by:
`p(x)=-2(x-9)^2+200`.

To find maximum number of fish, we use derivative test

`p(x)=-2(x-9)^2+200\\p'(x) =4(x-9)\\p`

Since second derivative is positive,

there will not be any maximum but only minimum

`2(x-9) =0x=9`

Minimum when x=9 and minimum population

p(x) =200

Maximum when x -infinity