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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+200p(x)=−2(x−9) 2 +200p, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, minus, 9, right parenthesis, start superscript, 2, end superscript, plus, 200 what is the maximum number of fish?

Respuesta :

carlosego
We have the following function:
 p (x) = - 2 (x-9) ^ 2 +200
 We derive to find the maximum of the function:
 p '(x) = - 4 (x-9)
 Rewriting:
 p '(x) = - 4x + 36
 We match zero:
 -4x + 36 = 0
 We clear x
 x = 36/4
 x = 9 degrees
 The maximum population occurs when x = 9.
 We evaluate the function for this value:
 p (9) = - 2 * (9-9) ^ 2 +200
 p (9) = 200
 Answer:
 The maximum number of fish is:
 p (9) = 200

The maximum number of fish is 200.

What is differentiation?

Differentiation is the reverse of integration.

The given function is;

[tex]\rm p(x)=-2(x-9)^2+200[/tex]

The maximum number of fish is determined in the following steps given below.

[tex]\rm p(x)=-2(x-9)^2+200\\\\ p '(x) = - 4 (x-9)\\\\ p '(x) = - 4 x-36\\\\ p '(x) = 0\\\\-4x+36=0\\\\-4x=-36\\\\x=\dfrac{-36}{-4}\\\\x=9[/tex]

Substitute the value of x in the function

[tex]\rm p(9)=-2(9-9)^2+200\\\\p(9)=0+200\\\\ p(9)=200[/tex]

Hence, the maximum number of fish is 200.

To know more about differentiation click the link given below.

https://brainly.com/question/10115447

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