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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?

Respuesta :

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

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: [tex]p(x)=-2(x-9)^2+200[/tex].

To find maximum number of fish, we use derivative test

[tex]p(x)=-2(x-9)^2+200\\p'(x) =4(x-9)\\p"(x)=4>0[/tex]

Since second derivative is positive,

there will not be any maximum but only minimum

[tex]2(x-9) =0x=9[/tex]

Minimum when x=9 and minimum population

p(x) =200

Maximum when x -infinity

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