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

Answer:

Step-by-step 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

$p(x)=-2(x-9)^2+200\\p'(x) =4(x-9)\\p"(x)=4>0$

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

Answer 2

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